{epsilon}-optimality conditions for weakly convex problems
Pappalardo, M.
1994-12-31
There are several generalizations concerning the concept of convexity both for sets and for functions. Weak convexity, among these, has showed many possibilities of applications and many theoretical properties. It has, in fact, been applied in several fields of mathematics: see for example geometry and optimization. We want to analyze this generalization of the concept of convexity via the image-space approach. This kind of approach has showed its utility in many fields of optimization. In particular, we introduce a new concept of {open_quotes}image{close_quotes} based on a suitable relaxation or reduction (lower and upper) of the image itself. Moreover we analyze the main properties of this concept and we show how to utilize it in the study of weakly convex constrained extremum problems in order to obtain {epsilon}-optimality conditions. The paper is divided in three parts: in the first we introduce the concept of perturbed image and we investigate the main theoretical properties. In the second we state {epsilon}-optimality conditions for weakly convex constrained extremum problems. In the third one we study relationships between this type of image and the augmented lagrangian.
Gradient vs. approximation design optimization techniques in low-dimensional convex problems
NASA Astrophysics Data System (ADS)
Fedorik, Filip
2013-10-01
Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.
A two-layer recurrent neural network for nonsmooth convex optimization problems.
Qin, Sitian; Xue, Xiaoping
2015-06-01
In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush-Kuhn-Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems.
Cheng, Long; Hou, Zeng-Guang; Lin, Yingzi; Tan, Min; Zhang, Wenjun Chris; Wu, Fang-Xiang
2011-05-01
A recurrent neural network is proposed for solving the non-smooth convex optimization problem with the convex inequality and linear equality constraints. Since the objective function and inequality constraints may not be smooth, the Clarke's generalized gradients of the objective function and inequality constraints are employed to describe the dynamics of the proposed neural network. It is proved that the equilibrium point set of the proposed neural network is equivalent to the optimal solution of the original optimization problem by using the Lagrangian saddle-point theorem. Under weak conditions, the proposed neural network is proved to be stable, and the state of the neural network is convergent to one of its equilibrium points. Compared with the existing neural network models for non-smooth optimization problems, the proposed neural network can deal with a larger class of constraints and is not based on the penalty method. Finally, the proposed neural network is used to solve the identification problem of genetic regulatory networks, which can be transformed into a non-smooth convex optimization problem. The simulation results show the satisfactory identification accuracy, which demonstrates the effectiveness and efficiency of the proposed approach.
ERIC Educational Resources Information Center
Berger, Marcel
1990-01-01
Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)
CVXPY: A Python-Embedded Modeling Language for Convex Optimization
Diamond, Steven; Boyd, Stephen
2016-01-01
CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples. PMID:27375369
CVXPY: A Python-Embedded Modeling Language for Convex Optimization.
Diamond, Steven; Boyd, Stephen
2016-04-01
CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.
Sparse recovery via convex optimization
NASA Astrophysics Data System (ADS)
Randall, Paige Alicia
This thesis considers the problem of estimating a sparse signal from a few (possibly noisy) linear measurements. In other words, we have y = Ax + z where A is a measurement matrix with more columns than rows, x is a sparse signal to be estimated, z is a noise vector, and y is a vector of measurements. This setup arises frequently in many problems ranging from MRI imaging to genomics to compressed sensing.We begin by relating our setup to an error correction problem over the reals, where a received encoded message is corrupted by a few arbitrary errors, as well as smaller dense errors. We show that under suitable conditions on the encoding matrix and on the number of arbitrary errors, one is able to accurately recover the message.We next show that we are able to achieve oracle optimality for x, up to a log factor and a factor of sqrt{s}, when we require the matrix A to obey an incoherence property. The incoherence property is novel in that it allows the coherence of A to be as large as O(1/ log n) and still allows sparsities as large as O(m/log n). This is in contrast to other existing results involving coherence where the coherence can only be as large as O(1/sqrt{m}) to allow sparsities as large as O(sqrt{m}). We also do not make the common assumption that the matrix A obeys a restricted eigenvalue condition.We then show that we can recover a (non-sparse) signal from a few linear measurements when the signal has an exactly sparse representation in an overcomplete dictionary. We again only require that the dictionary obey an incoherence property.Finally, we introduce the method of l_1 analysis and show that it is guaranteed to give good recovery of a signal from a few measurements, when the signal can be well represented in a dictionary. We require that the combined measurement/dictionary matrix satisfies a uniform uncertainty principle and we compare our results with the more standard l_1 synthesis approach.All our methods involve solving an l_1 minimization
First and second order convex approximation strategies in structural optimization
NASA Technical Reports Server (NTRS)
Fleury, C.
1989-01-01
In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.
The Convex Geometry of Linear Inverse Problems
2010-12-02
The Convex Geometry of Linear Inverse Problems Venkat Chandrasekaranm, Benjamin Rechtw, Pablo A. Parrilom, and Alan S. Willskym ∗ m Laboratory for...83) = 3r(m1 +m2 − r) + 2(m1 − r − r2) (84) where the second inequality follows from the fact that (a+ b)2 ≤ 2a2 + 2b2. References [1] Aja- Fernandez , S
Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization
NASA Astrophysics Data System (ADS)
Yamagishi, Masao; Yamada, Isao
2017-04-01
Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.
Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization
NASA Technical Reports Server (NTRS)
Pinson, Robin; Lu, Ping
2015-01-01
This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.
Approximate proximal point methods for convex programming problems
Eggermont, P.
1994-12-31
We study proximal point methods for the finite dimensional convex programming problem minimize f(x) such that x {element_of} C, where f : dom f {contained_in} RIR is a proper convex function and C {contained_in} R is a closed convex set.
NASA Astrophysics Data System (ADS)
Pospelov, A. I.
2016-08-01
Adaptive methods for the polyhedral approximation of the convex Edgeworth-Pareto hull in multiobjective monotone integer optimization problems are proposed and studied. For these methods, theoretical convergence rate estimates with respect to the number of vertices are obtained. The estimates coincide in order with those for filling and augmentation H-methods intended for the approximation of nonsmooth convex compact bodies.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Non-convex Statistical Optimization for Sparse Tensor Graphical Model
Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang
2016-01-01
We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies.
From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation
Egozcue, J. Meziat, R. Pedregal, P.
2002-12-19
We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.
Statistical Mechanics of Optimal Convex Inference in High Dimensions
NASA Astrophysics Data System (ADS)
Advani, Madhu; Ganguli, Surya
2016-07-01
A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α =(N /P )→∞ . However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α . We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
NASA Astrophysics Data System (ADS)
Geletu, Abebe; Klöppel, Michael; Hoffmann, Armin; Li, Pu
2015-04-01
Chance constrained optimization problems in engineering applications possess highly nonlinear process models and non-convex structures. As a result, solving a nonlinear non-convex chance constrained optimization (CCOPT) problem remains as a challenging task. The major difficulty lies in the evaluation of probability values and gradients of inequality constraints which are nonlinear functions of stochastic variables. This article proposes a novel analytic approximation to improve the tractability of smooth non-convex chance constraints. The approximation uses a smooth parametric function to define a sequence of smooth nonlinear programs (NLPs). The sequence of optimal solutions of these NLPs remains always feasible and converges to the solution set of the CCOPT problem. Furthermore, Karush-Kuhn-Tucker (KKT) points of the approximating problems converge to a subset of KKT points of the CCOPT problem. Another feature of this approach is that it can handle uncertainties with both Gaussian and/or non-Gaussian distributions.
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; Bochev, Pavel; Shashkov, Mikhail
2016-02-24
Here, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. Also, this volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
Estimation of Saxophone Control Parameters by Convex Optimization
Wang, Cheng-i; Smyth, Tamara; Lipton, Zachary C.
2015-01-01
In this work, an approach to jointly estimating the tone hole configuration (fingering) and reed model parameters of a saxophone is presented. The problem isn't one of merely estimating pitch as one applied fingering can be used to produce several different pitches by bugling or overblowing. Nor can a fingering be estimated solely by the spectral envelope of the produced sound (as it might for estimation of vocal tract shape in speech) since one fingering can produce markedly different spectral envelopes depending on the player's embouchure and control of the reed. The problem is therefore addressed by jointly estimating both the reed (source) parameters and the fingering (filter) of a saxophone model using convex optimization and 1) a bank of filter frequency responses derived from measurement of the saxophone configured with all possible fingerings and 2) sample recordings of notes produced using all possible fingerings, played with different overblowing, dynamics and timbre. The saxophone model couples one of several possible frequency response pairs (corresponding to the applied fingering), and a quasi-static reed model generating input pressure at the mouthpiece, with control parameters being blowing pressure and reed stiffness. Applied fingering and reed parameters are estimated for a given recording by formalizing a minimization problem, where the cost function is the error between the recording and the synthesized sound produced by the model having incremental parameter values for blowing pressure and reed stiffness. The minimization problem is nonlinear and not differentiable and is made solvable using convex optimization. The performance of the fingering identification is evaluated with better accuracy than previous reported value. PMID:27754493
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...
2016-02-24
Here, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. Also, this volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problemmore » in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less
NASA Astrophysics Data System (ADS)
Chernyaev, Yu. A.
2016-10-01
The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.
NASA Astrophysics Data System (ADS)
Pinson, Robin Marie
Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed
The Existence Problem for Steiner Networks in Strictly Convex Domains
NASA Astrophysics Data System (ADS)
Freire, Alexandre
2011-05-01
We consider the existence problem for `Steiner networks' (trivalent graphs with 2 π/3 angles at each junction) in strictly convex domains, with `Neumann' boundary conditions. For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit examples of nonexistence are given.
Lagrange Duality Theory for Convex Control Problems,
to be optimal is also given. The dual variables p and v corresponding to the system dynamics and state constraints are proved to be of bounded ... variation while the multiplier corresponding to the control constraints is proved to lie in 1. Finally, a control and state minimum principle is proved. If
Directional Convexity and Finite Optimality Conditions.
1984-03-01
2664 DAAG29-80-C-0041 UNCLASSIFIED F/G 12/1 NLflflflflflII 1226 1.4 4 111111_L25__-6 MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU Of STANDARDS 196 A...system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...u,-) to reach a boundary point of R(T) at time T [2,7,8]. All of these conditions are obtained from a local analysis: to test the optimality of a
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
ZHANG ¶ Abstract. It has been shown in [14] that the accelerated prox-level ( APL ) method and its variant, the uniform smoothing level (USL) method...introduce two new variants of level methods, i.e., the fast APL (FAPL) method and the fast USL (FUSL) method, for solving large scale black-box and...structured convex programming problems respectively. Both FAPL and FUSL enjoy the same optimal iteration complexity as APL and USL, while the number of
Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids
NASA Technical Reports Server (NTRS)
Pinson, Robin M.; Lu, Ping
2016-01-01
Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.
Numerical optimization method for packing regular convex polygons
NASA Astrophysics Data System (ADS)
Galiev, Sh. I.; Lisafina, M. S.
2016-08-01
An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.
Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods
2016-11-16
best sensors after an optimization procedure. Due to the positive definite nature of the Fisher information matrix, convex optimization may be used to...parametrized to select the best sensors after an optimization procedure. Due to the positive definite nature of the Fisher information matrix, convex op...Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6180--16-9711 Using Fisher Information Criteria for Chemical Sensor Selection via Convex
Multiband RF pulses with improved performance via convex optimization.
Shang, Hong; Larson, Peder E Z; Kerr, Adam; Reed, Galen; Sukumar, Subramaniam; Elkhaled, Adam; Gordon, Jeremy W; Ohliger, Michael A; Pauly, John M; Lustig, Michael; Vigneron, Daniel B
2016-01-01
Selective RF pulses are commonly designed with the desired profile as a low pass filter frequency response. However, for many MRI and NMR applications, the spectrum is sparse with signals existing at a few discrete resonant frequencies. By specifying a multiband profile and releasing the constraint on "don't-care" regions, the RF pulse performance can be improved to enable a shorter duration, sharper transition, or lower peak B1 amplitude. In this project, a framework for designing multiband RF pulses with improved performance was developed based on the Shinnar-Le Roux (SLR) algorithm and convex optimization. It can create several types of RF pulses with multiband magnitude profiles, arbitrary phase profiles and generalized flip angles. The advantage of this framework with a convex optimization approach is the flexible trade-off of different pulse characteristics. Designs for specialized selective RF pulses for balanced SSFP hyperpolarized (HP) (13)C MRI, a dualband saturation RF pulse for (1)H MR spectroscopy, and a pre-saturation pulse for HP (13)C study were developed and tested.
Convex hull or crossing avoidance? Solution heuristics in the traveling salesperson problem.
MacGregor, James N; Chronicle, Edward P; Ormerod, Thomas C
2004-03-01
Untrained adults appear to have access to cognitive processes that allow them to perform well in the Euclidean version of the traveling salesperson problem (E-TSP). They do so despite the famous computational intractability of the problem, which stems from its combinatorial complexity. A current hypothesis is the humans' good performance is based on following a strategy of connecting boundary points in order (the convex hull hypothesis). Recently, an alternative has been proposed, that performance is governed by a strategy of avoiding crossings. We examined the crossing avoidance hypothesis from the perspectives of its capacity to explain existing data, its theoretical adequacy, and its ability to explain the results of three new experiments. In Experiment 1, effects on the solution quality of number of points versus number of interior points were compared. In Experiment 2, the distributions of observed paths were compared with those predicted from the two hypotheses. In Experiment 3, figural effects were varied to induce crossings. The results of the experiments were more consistent with the convex hull than with the crossing avoidance hypothesis. Despite its simplicity and intuitive appeal, crossing avoidance does not provide a complete alternative to the convex hull hypothesis. Further elucidation of human strategies and heuristics for optimization problems such as the E-TSP will aid our understanding of how cognitive processes have adapted to the demands of combinatorial difficulty.
Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems
NASA Astrophysics Data System (ADS)
Kuterin, F. A.; Sumin, M. I.
2017-01-01
A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and, hence, the instability of the classical Lagrange principle for it to its regularity properties and the subdifferentiability of the value function in the problem is discussed. An iterative nondifferential Lagrange principle with a stopping rule is proved for the indicated problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimization problems is discussed. The capabilities of this principle are illustrated by numerically solving the classical ill-posed problem of finding the normal solution of a Fredholm integral equation of the first kind.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yin, Chuancun; Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem.
Al-Mulhem, M; Al-Maghrabi, T
1998-01-01
This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.
An uncertain multidisciplinary design optimization method using interval convex models
NASA Astrophysics Data System (ADS)
Li, Fangyi; Luo, Zhen; Sun, Guangyong; Zhang, Nong
2013-06-01
This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss-Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.
Huang, Kuo -Ling; Mehrotra, Sanjay
2016-11-08
We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less
Huang, Kuo -Ling; Mehrotra, Sanjay
2016-11-08
We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).
A Localization Method for Multistatic SAR Based on Convex Optimization.
Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
A Localization Method for Multistatic SAR Based on Convex Optimization
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function’s maximum is on the circumference of the ellipse which is the iso-range for its model function’s T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment. PMID:26566031
Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization
NASA Astrophysics Data System (ADS)
Baldwin, Charles; Riofrio, Carlos; Deutsch, Ivan
2013-03-01
Quantum process tomography (QPT) is an essential tool to diagnose the implementation of a dynamical map. However, the standard protocol is extremely resource intensive. For a Hilbert space of dimension d, it requires d2 different input preparations followed by state tomography via the estimation of the expectation values of d2 - 1 orthogonal observables. We show that when the process is nearly unitary, we can dramatically improve the efficiency and robustness of QPT through a collective continuous measurement protocol on an ensemble of identically prepared systems. Given the measurement history we obtain the process matrix via a convex program that optimizes a desired cost function. We study two estimators: least-squares and compressive sensing. Both allow rapid QPT due to the condition of complete positivity of the map; this is a powerful constraint to force the process to be physical and consistent with the data. We apply the method to a real experimental implementation, where optimal control is used to perform a unitary map on a d = 8 dimensional system of hyperfine levels in cesium atoms, and obtain the measurement record via Faraday spectroscopy of a laser probe. Supported by the NSF
Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids
NASA Technical Reports Server (NTRS)
Pinson, Robin M.; Lu, Ping
2016-01-01
Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The
A One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.
Qin, Sitian; Feng, Jiqiang; Song, Jiahui; Wen, Xingnan; Xu, Chen
2016-12-22
In this paper, based on CR calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence. Some numerical examples and application are presented to substantiate the effectiveness of the proposed neural network.
Gálvez, Akemi; Iglesias, Andrés
2013-01-01
Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380
Ambikapathi, ArulMurugan; Chan, Tsung-Han; Lin, Chia-Hsiang; Yang, Fei-Shih; Chi, Chong-Yung; Wang, Yue
2016-04-01
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a powerful imaging modality to study the pharmacokinetics in a suspected cancer/tumor tissue. The pharmacokinetic (PK) analysis of prostate cancer includes the estimation of time activity curves (TACs), and thereby, the corresponding kinetic parameters (KPs), and plays a pivotal role in diagnosis and prognosis of prostate cancer. In this paper, we endeavor to develop a blind source separation algorithm, namely convex-optimization-based KPs estimation (COKE) algorithm for PK analysis based on compartmental modeling of DCE-MRI data, for effective prostate tumor detection and its quantification. The COKE algorithm first identifies the best three representative pixels in the DCE-MRI data, corresponding to the plasma, fast-flow, and slow-flow TACs, respectively. The estimation accuracy of the flux rate constants (FRCs) of the fast-flow and slow-flow TACs directly affects the estimation accuracy of the KPs that provide the cancer and normal tissue distribution maps in the prostate region. The COKE algorithm wisely exploits the matrix structure (Toeplitz, lower triangular, and exponential decay) of the original nonconvex FRCs estimation problem, and reformulates it into two convex optimization problems that can reliably estimate the FRCs. After estimation of the FRCs, the KPs can be effectively estimated by solving a pixel-wise constrained curve-fitting (convex) problem. Simulation results demonstrate the efficacy of the proposed COKE algorithm. The COKE algorithm is also evaluated with DCE-MRI data of four different patients with prostate cancer and the obtained results are consistent with clinical observations.
Convex Optimization Methods for Graphs and Statistical Modeling
2011-06-01
extraneous polylogarithmic factors. In the next section we describe a new mechanism for estimating Gaussian widths, which provides near-optimal guarantees...so-called Quadratic Assignment Problem (QAP) [32]. Solving QAP is hard in general, because it includes as a special case the Hamiltonian cycle problem...only if the graph contains a Hamiltonian cycle. However there are well-studied spectral and semidefinite relaxations for QAP, which we discuss next
Mehrotra, Sanjay; Papp, Dávid
2014-01-01
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.
Mehrotra, Sanjay; Papp, Dávid
2014-01-01
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robustmore » optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.« less
Implementation of a Point Algorithm for Real-Time Convex Optimization
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Motaghedi, Shui; Carson, John
2007-01-01
The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.
Scalable analysis of nonlinear systems using convex optimization
NASA Astrophysics Data System (ADS)
Papachristodoulou, Antonis
In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques. After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non-polynomial vector fields and switching systems, as well estimating the region of attraction and the L2 gain can be treated in a unified manner. We apply our results to examples from biology and aerospace. We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time-delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given. The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST---a recently developed network congestion control scheme---so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way. Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of
NASA Astrophysics Data System (ADS)
Acker, A.
Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.
Higher order sensitivity of solutions to convex programming problems without strict complementarity
NASA Technical Reports Server (NTRS)
Malanowski, Kazimierz
1988-01-01
Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.
Le Thi, Hoai An; Vo, Xuan Thanh; Pham Dinh, Tao
2014-11-01
In this paper, we consider the problem of feature selection for linear SVMs on uncertain data that is inherently prevalent in almost all datasets. Using principles of Robust Optimization, we propose robust schemes to handle data with ellipsoidal model and box model of uncertainty. The difficulty in treating ℓ0-norm in feature selection problem is overcome by using appropriate approximations and Difference of Convex functions (DC) programming and DC Algorithms (DCA). The computational results show that the proposed robust optimization approaches are superior than a traditional approach in immunizing perturbation of the data.
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
Gan, LW; Li, N; Topcu, U; Low, SH
2015-01-01
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.
NASA Astrophysics Data System (ADS)
Wei, W. B.; Tan, L.; Jia, M. Q.; Pan, Z. K.
2017-01-01
The variational level set method is one of the main methods of image segmentation. Due to signed distance functions as level sets have to keep the nature of the functions through numerical remedy or additional technology in an evolutionary process, it is not very efficient. In this paper, a normal vector projection method for image segmentation using Chan-Vese model is proposed. An equivalent formulation of Chan-Vese model is used by taking advantage of property of binary level set functions and combining with the concept of convex relaxation. Threshold method and projection formula are applied in the implementation. It can avoid the above problems and obtain a global optimal solution. Experimental results on both synthetic and real images validate the effects of the proposed normal vector projection method, and show advantages over traditional algorithms in terms of computational efficiency.
Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir
2014-11-06
Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.
Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang; Chen, Ken Chung; Shen, Steve G. F.; Yan, Jin; Lee, Philip K. M.; Chow, Ben; Liu, Nancy X.; Xia, James J.; Shen, Dinggang
2014-04-15
Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT
SLOPE—ADAPTIVE VARIABLE SELECTION VIA CONVEX OPTIMIZATION
Bogdan, Małgorzata; van den Berg, Ewout; Sabatti, Chiara; Su, Weijie; Candès, Emmanuel J.
2015-01-01
We introduce a new estimator for the vector of coefficients β in the linear model y = Xβ + z, where X has dimensions n × p with p possibly larger than n. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to minb∈ℝp12‖y−Xb‖ℓ22+λ1|b|(1)+λ2|b|(2)+⋯+λp|b|(p),where λ1 ≥ λ2 ≥ … ≥ λp ≥ 0 and |b|(1)≥|b|(2)≥⋯≥|b|(p) are the decreasing absolute values of the entries of b. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical ℓ1 procedures such as the Lasso. Here, the regularizer is a sorted ℓ1 norm, which penalizes the regression coefficients according to their rank: the higher the rank—that is, stronger the signal—the larger the penalty. This is similar to the Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] procedure (BH) which compares more significant p-values with more stringent thresholds. One notable choice of the sequence {λi} is given by the BH critical values λBH(i)=z(1−i⋅q/2p), where q ∈ (0, 1) and z(α) is the quantile of a standard normal distribution. SLOPE aims to provide finite sample guarantees on the selected model; of special interest is the false discovery rate (FDR), defined as the expected proportion of irrelevant regressors among all selected predictors. Under orthogonal designs, SLOPE with λBH provably controls FDR at level q. Moreover, it also appears to have appreciable inferential properties under more general designs X while having substantial power, as demonstrated in a series of experiments running on both simulated and real data. PMID:26709357
Convex Optimization of Coincidence Time Resolution for a High-Resolution PET System
Reynolds, Paul D.; Olcott, Peter D.; Pratx, Guillem; Lau, Frances W. Y.
2013-01-01
We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3’s analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n3) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ± 0.07 ns full-width at half-maximum (FWHM) to 6.92 ± 0.02 ns FWHM (11.52 ± 0.05 ns to 4.89 ± 0.02 ns for unpaired photons). PMID:20876008
The Optimal Partial Transport Problem
NASA Astrophysics Data System (ADS)
Figalli, Alessio
2010-02-01
Given two densities f and g, we consider the problem of transporting a fraction {m in [0,min\\{\\|f\\|_{L^1},\\|g\\|_{L^1}\\}]} of the mass of f onto g minimizing a transportation cost. If the cost per unit of mass is given by | x - y|2, we will see that uniqueness of solutions holds for {m in [\\|fwedge g\\|_{L^1},min\\{\\|f\\|_{L^1},\\|g\\|_{L^1}\\}]} . This extends the result of C affarelli and M cCann in Ann Math (in print), where the authors consider two densities with disjoint supports. The free boundaries of the active regions are shown to be ( n - 1)-rectifiable (provided the supports of f and g have Lipschitz boundaries), and under some weak regularity assumptions on the geometry of the supports they are also locally semiconvex. Moreover, assuming f and g supported on two bounded strictly convex sets {{Ω,Λ subset mathbb {R}^n}} , and bounded away from zero and infinity on their respective supports, {C^{0,α}_loc} regularity of the optimal transport map and local C 1 regularity of the free boundaries away from {{Ω\\cap Λ}} are shown. Finally, the optimal transport map extends to a global homeomorphism between the active regions.
Van Rooij, Iris; Stege, Ulrike; Schactman, Alissa
2003-03-01
Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature so far, there is no evidence for this hypothesis. Alternatively we propose and motivate the hypothesis that people aim at avoiding crossings.
Vickers, Douglas; Lee, Michael D; Dry, Matthew; Hughes, Peter
2003-10-01
The planar Euclidean version of the traveling salesperson problem requires finding the shortest tour through a two-dimensional array of points. MacGregor and Ormerod (1996) have suggested that people solve such problems by using a global-to-local perceptual organizing process based on the convex hull of the array. We review evidence for and against this idea, before considering an alternative, local-to-global perceptual process, based on the rapid automatic identification of nearest neighbors. We compare these approaches in an experiment in which the effects of number of convex hull points and number of potential intersections on solution performance are measured. Performance worsened with more points on the convex hull and with fewer potential intersections. A measure of response uncertainty was unaffected by the number of convex hull points but increased with fewer potential intersections. We discuss a possible interpretation of these results in terms of a hierarchical solution process based on linking nearest neighbor clusters.
Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis
NASA Astrophysics Data System (ADS)
Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Yan, Ruqiang
2016-12-01
The bearing failure, generating harmful vibrations, is one of the most frequent reasons for machine breakdowns. Thus, performing bearing fault diagnosis is an essential procedure to improve the reliability of the mechanical system and reduce its operating expenses. Most of the previous studies focused on rolling bearing fault diagnosis could be categorized into two main families, kurtosis-based filter method and wavelet-based shrinkage method. Although tremendous progresses have been made, their effectiveness suffers from three potential drawbacks: firstly, fault information is often decomposed into proximal frequency bands and results in impulsive feature frequency band splitting (IFFBS) phenomenon, which significantly degrades the performance of capturing the optimal information band; secondly, noise energy spreads throughout all frequency bins and contaminates fault information in the information band, especially under the heavy noisy circumstance; thirdly, wavelet coefficients are shrunk equally to satisfy the sparsity constraints and most of the feature information energy are thus eliminated unreasonably. Therefore, exploiting two pieces of prior information (i.e., one is that the coefficient sequences of fault information in the wavelet basis is sparse, and the other is that the kurtosis of the envelope spectrum could evaluate accurately the information capacity of rolling bearing faults), a novel weighted sparse model and its corresponding framework for bearing fault diagnosis is proposed in this paper, coined KurWSD. KurWSD formulates the prior information into weighted sparse regularization terms and then obtains a nonsmooth convex optimization problem. The alternating direction method of multipliers (ADMM) is sequentially employed to solve this problem and the fault information is extracted through the estimated wavelet coefficients. Compared with state-of-the-art methods, KurWSD overcomes the three drawbacks and utilizes the advantages of both family
Zhang, Bo; Sun, Jiwei; Wang, Qin; Fan, Niansi; Ni, Jialing; Li, Weicheng; Gao, Yingxin; Li, Yu-You; Xu, Changyou
2017-01-12
The electro-Fenton treatment of coking wastewater was evaluated experimentally in a batch electrochemical reactor. Based on central composite design coupled with response surface methodology, a regression quadratic equation was developed to model the total organic carbon (TOC) removal efficiency. This model was further proved to accurately predict the optimization of process variables by means of analysis of variance. With the aid of the convex optimization method, which is a global optimization method, the optimal parameters were determined as current density of 30.9 mA/cm(2), Fe(2+) concentration of 0.35 mg/L, and pH of 4.05. Under the optimized conditions, the corresponding TOC removal efficiency was up to 73.8%. The maximum TOC removal efficiency achieved can be further confirmed by the results of gas chromatography-mass spectrum analysis.
NASA Astrophysics Data System (ADS)
Acker, A.
We give an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity μ >0 is embedded in a closed irrotational flow inside a closed, convex vessel in ℜ 2. The unknown boundary of the vortex core is a closed curve Γ along which (v+)^2-(v^-)^2=Λ , where v+ and v- denote, respectively, the exterior and interior flow-speeds along Γ and Λ is a given constant. Our existence results all apply to the natural multidimensional mathematical generalization of the above problem. The present existence theorems are the only ones available for the Prandtl-Batchelor problem for Λ >0, because (a) the author's prior existence treatment was restricted to the case where Λ <0, and because (b) there is no analytical existence theory available for this problem in the non-convex case, regardless of the sign of Λ .
Optimal structural design via optimality criteria as a nonsmooth mechanics problem
NASA Astrophysics Data System (ADS)
Tzaferopoulos, M. Ap.; Stravroulakis, G. E.
1995-06-01
In the theory of plastic structural design via optimality criteria (due to W. Prager), the optimal design problem is transformed to a nonlinear elastic structural analysis problem with appropriate stress-strain laws, which generally include complete vertical branches. In this context, the concept of structural universe (in the sense of G. Rozvany) permits the treatment of complicated optimal layout problems. Recent progress in the field of nonsmooth mechanics makes the solution of structural analysis problems with this kind of 'complete' law possible. Elements from the two fields are combined in this paper for the solution of optimal design and layout problems for structures. The optimal layout of plane trusses with various specific cost functions is studied here as a representative problem. The use of convex, continuous and piecewise linear specific cost functions for the structural members leads to problems of linear variational inequalities or equivalently piecewise linear, convex but nonsmooth optimization problems, which are solved by means of an iterative algorithm based on sequential linear programming techniques. Numerical examples illustrate the theory and its applicability to practical engineering structures. Following a parametric investigation of an optimal bridge design, certain aspects of the optimal truss layout problem are discussed, which can be extended to other types of structural systems as well.
Bi-convex Optimization to Learn Classifiers from Multiple Biomedical Annotations.
Wang, Xin; Bi, Jinbo
2016-06-07
The problem of constructing classifiers from multiple annotators who provide inconsistent training labels is important and occurs in many application domains. Many existing methods focus on the understanding and learning of the crowd behaviors. Several probabilistic algorithms consider the construction of classifiers for specific tasks using consensus of multiple labelers annotations. These methods impose a prior on the consensus and develop an expectation-maximization algorithm based on logistic regression loss. We extend the discussion to the hinge loss commonly used by support vector machines. Our formulations form bi-convex programs that construct classifiers and estimate the reliability of each labeler simultaneously. Each labeler is associated with a reliability parameter, which can be a constant, or class-dependent, or varies for different examples. The hinge loss is modified by replacing the true labels by the weighted combination of labelers' labels with reliabilities as weights. Statistical justification is discussed to motivate the use of linear combination of labels. In parallel to the expectation-maximization algorithm for logistic based methods, efficient alternating algorithms are developed to solve the proposed bi-convex programs. Experimental results on benchmark datasets and three real-world biomedical problems demonstrate that the proposed methods either outperform or are competitive to the state of the art.
Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization
NASA Technical Reports Server (NTRS)
Pinson, Robin; Lu, Ping
2015-01-01
Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on-board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles.
NASA Astrophysics Data System (ADS)
Huang, Wenxuan; Kitchaev, Daniil A.; Dacek, Stephen T.; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-10-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.
Class and Home Problems: Optimization Problems
ERIC Educational Resources Information Center
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces
NASA Astrophysics Data System (ADS)
Jin, Qinian; Lu, Xiliang
2014-04-01
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.
Fast inference of ill-posed problems within a convex space
NASA Astrophysics Data System (ADS)
Fernandez-de-Cossio-Diaz, J.; Mulet, R.
2016-07-01
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope. In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a genome scale Escherichia coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.
Convex hull based neuro-retinal optic cup ellipse optimization in glaucoma diagnosis.
Zhang, Zhuo; Liu, Jiang; Cherian, Neetu Sara; Sun, Ying; Lim, Joo Hwee; Wong, Wing Kee; Tan, Ngan Meng; Lu, Shijian; Li, Huiqi; Wong, Tien Ying
2009-01-01
Glaucoma is the second leading cause of blindness. Glaucoma can be diagnosed through measurement of neuro-retinal optic cup-to-disc ratio (CDR). Automatic calculation of optic cup boundary is challenging due to the interweavement of blood vessels with the surrounding tissues around the cup. A Convex Hull based Neuro-Retinal Optic Cup Ellipse Optimization algorithm improves the accuracy of the boundary estimation. The algorithm's effectiveness is demonstrated on 70 clinical patient's data set collected from Singapore Eye Research Institute. The root mean squared error of the new algorithm is 43% better than the ARGALI system which is the state-of-the-art. This further leads to a large clinical evaluation of the algorithm involving 15 thousand patients from Australia and Singapore.
A Problem on Optimal Transportation
ERIC Educational Resources Information Center
Cechlarova, Katarina
2005-01-01
Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…
2012-02-09
several optimization models and algorithm design for problems from computer vision and learning , research on sparse solutions in quadratic optimization...following papers: [9] L. Mukherjee, V. Singh, J. Peng and C. Hinrichs. Learning kernels for variants of normalized cuts: Convex relaxations and...are very small gaps compared to state-of-the-art knowledge in comunications . Table 1. Bounds for adjacency matrix
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants
NASA Astrophysics Data System (ADS)
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-01
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient’s anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant’s RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B1+ field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient’s anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants.
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-21
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient's anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant's RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B(1)(+) field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient's anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.
1982-12-21
Operations Research, Vol. 18, No. 1, pp. 107-118. FENCHEL , W. (1953). Convex Cones , Sets and Functions . Lecture Notes, Princeton University Press... FUNCTION AND CONVEXITY PROPERTIES OF THE SOLUTION SET MAP ..... .............. ... 40 5. CONCLUDING REMARKS ................ ...... 48 REFERENCES...I * -3- T-471 is the set conv(A) - {x1 + (l-X)x 12 XX 2 e A, A [0,1]1 . The set K CEr is a cone if x e K implies x e K for all > 0 ,and K is a convex
Automatic Treatment Planning with Convex Imputing
NASA Astrophysics Data System (ADS)
Sayre, G. A.; Ruan, D.
2014-03-01
Current inverse optimization-based treatment planning for radiotherapy requires a set of complex DVH objectives to be simultaneously minimized. This process, known as multi-objective optimization, is challenging due to non-convexity in individual objectives and insufficient knowledge in the tradeoffs among the objective set. As such, clinical practice involves numerous iterations of human intervention that is costly and often inconsistent. In this work, we propose to address treatment planning with convex imputing, a new-data mining technique that explores the existence of a latent convex objective whose optimizer reflects the DVH and dose-shaping properties of previously optimized cases. Using ten clinical prostate cases as the basis for comparison, we imputed a simple least-squares problem from the optimized solutions of the prostate cases, and show that the imputed plans are more consistent than their clinical counterparts in achieving planning goals.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
NASA Technical Reports Server (NTRS)
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
NASA Astrophysics Data System (ADS)
Liolios, K.; Georgiev, I.; Liolios, A.
2012-10-01
A numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soil-pipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the non-convex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and a non-convex linear complementarity problem is solved in each time-step.
Optimization and geophysical inverse problems
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness
More on conditions of local and global minima coincidence in discrete optimization problems
Lebedeva, T.T.; Sergienko, I.V.; Soltan, V.P.
1994-05-01
In some areas of discrete optimization, it is necessary to isolate classes of problems whose target functions do not have local or strictly local minima that differ from the global minima. Examples include optimizations on discrete metric spaces and graphs, lattices and partially ordered sets, and linear combinatorial problems. A unified schema that to a certain extent generalizes the convexity models on which the above-cited works are based has been presented in articles. This article is a continuation of that research.
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
A novel neural network for nonlinear convex programming.
Gao, Xing-Bao
2004-05-01
In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Robust Utility Maximization Under Convex Portfolio Constraints
Matoussi, Anis; Mezghani, Hanen Mnif, Mohamed
2015-04-15
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.
Basic Studies in Combinatorial and Nondifferentiable Optimization.
1978-03-01
control problems with linear dynamics, convex cost, and convex inequality state and control constraints is analyzed...points. S.K. MITTER, Lagrange Duality Theory for Convex Control Problems , (with W.W. Hager), Journal of Control and Optimization , 14, August 1976, pp...Lagrange Duality Theory for Convex Control Problems ,” Journal of Control and Optimization , 14, August 1976, pp. 843—856. T.
NASA Astrophysics Data System (ADS)
Kupeev, Konstantin Y.; Wolfson, Haim J.
1995-08-01
Often objects which are not convex in the mathematical sense are treated as `perceptually convex'. We present an algorithm for recognition of the perceptual convexity of a 2D contour. We start by reducing the notion of `a contour is perceptually convex' to the notion of `a contour is Y-convex'. The latter reflects an absence of large concavities in the OY direction of an XOY frame. Then we represented a contour by a G-graph and modify the slowest descent-- the small leaf trimming procedure recently introduced for the estimation of shape similarity. We prove that executing the slowest descent dow to a G-graph consisting of 3 vertices allows us to detect large concavities in the OY direction. This allows us to recognize the perceptual convexity of an input contour.
Cheung, Ngaam J; Shen, Hong-Bin
2014-11-01
The stable conformation of a molecule is greatly important to uncover the secret of its properties and functions. Generally, the conformation of a molecule will be the most stable when it is of the minimum potential energy. Accordingly, the determination of the conformation can be solved in the optimization framework. It is, however, not an easy task to achieve the only conformation with the lowest energy among all the potential ones because of the high complexity of the energy landscape and the exponential computation increasing with molecular size. In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy. The proposed method is evaluated over a scalable simplified molecular potential energy function with up to 200 degrees of freedom and a realistic energy function of pseudo-ethane molecule. The experimental results are compared with other six PSO variants and four genetic algorithms. The results show HHPSO is significantly better than the compared PSOs with p-value less than 0.01277 over molecular potential energy function.
Convex Formulations of Learning from Crowds
NASA Astrophysics Data System (ADS)
Kajino, Hiroshi; Kashima, Hisashi
It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.
Convex Banding of the Covariance Matrix.
Bien, Jacob; Bunea, Florentina; Xiao, Luo
2016-01-01
We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.
Xia, Youshen; Feng, Gang; Wang, Jun
2008-08-01
This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush-Kuhn-Tucker point in the sense of Lyapunov and its output trajectory is globally convergent to a minimum solution. Compared with variety of the existing projection neural networks, including their extensions and modification, for solving such nonlinearly constrained optimization problems, it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point. Simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems.
ERIC Educational Resources Information Center
Tak, Susanne; Plaisier, Marco; van Rooij, Iris
2008-01-01
To explain human performance on the "Traveling Salesperson" problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors…
Numerical Optimization of Synergetic Maneuvers
1994-06-01
optimality conditions is termed the Karush-Kuln-Tucker ( KKT ) conditions . These necessary ...CONVERGENCE ................................................. 15 1. Su mnary Of Convexity and Optimality Conditions .............................. 15 2...point x. A point x* is called the optimal solution to the problem. 14 B. ALGORITHMS AND CONVERGENCE 1. Summary of Convexity and Optimality Conditions
First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
Bonnans, J. Frederic; Silva, Francisco J.
2012-06-15
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems
NASA Astrophysics Data System (ADS)
Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao
Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.
Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; McLeod, Jonathan; Chen, Yimin; de Ribaupierre, Sandrine; Fenster, Aaron
2015-02-01
A three-dimensional (3-D) ultrasound (US) system has been developed to monitor the intracranial ventricular system of preterm neonates with intraventricular hemorrhage (IVH) and the resultant dilation of the ventricles (ventriculomegaly). To measure ventricular volume from 3-D US images, a semi-automatic convex optimization-based approach is proposed for segmentation of the cerebral ventricular system in preterm neonates with IVH from 3-D US images. The proposed semi-automatic segmentation method makes use of the convex optimization technique supervised by user-initialized information. Experiments using 58 patient 3-D US images reveal that our proposed approach yielded a mean Dice similarity coefficient of 78.2% compared with the surfaces that were manually contoured, suggesting good agreement between these two segmentations. Additional metrics, the mean absolute distance of 0.65 mm and the maximum absolute distance of 3.2 mm, indicated small distance errors for a voxel spacing of 0.22 × 0.22 × 0.22 mm(3). The Pearson correlation coefficient (r = 0.97, p < 0.001) indicated a significant correlation of algorithm-generated ventricular system volume (VSV) with the manually generated VSV. The calculated minimal detectable difference in ventricular volume change indicated that the proposed segmentation approach with 3-D US images is capable of detecting a VSV difference of 6.5 cm(3) with 95% confidence, suggesting that this approach might be used for monitoring IVH patients' ventricular changes using 3-D US imaging. The mean segmentation times of the graphics processing unit (GPU)- and central processing unit-implemented algorithms were 50 ± 2 and 205 ± 5 s for one 3-D US image, respectively, in addition to 120 ± 10 s for initialization, less than the approximately 35 min required by manual segmentation. In addition, repeatability experiments indicated that the intra-observer variability ranges from 6.5% to 7.5%, and the inter-observer variability is 8.5% in terms
NASA Astrophysics Data System (ADS)
da Gama, Rogério Martins Saldanha
2015-10-01
In this paper, we study the steady-state (coupled) conduction-radiation heat transfer phenomenon in a non-convex opaque blackbody with temperature-dependent thermal conductivity. The mathematical description consists of a nonlinear partial differential equation subjected to a nonlinear boundary condition involving an integral operator that is inherently associated with the non-convexity of the body. The unknown is the absolute temperature distribution. The problem is rewritten with the aid of a Kirchhoff transformation, giving rise to linear partial differential equation and a new unknown. An iterative procedure is proposed for constructing the solution of the problem by means of a sequence of problems, each of them with an equivalent minimum principle. Proofs of convergence as well as existence and uniqueness of the solution are presented. An error estimate, for each element of the sequence, is presented too.
Constrained Graph Optimization: Interdiction and Preservation Problems
Schild, Aaron V
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
A Mathematical Optimization Problem in Bioinformatics
ERIC Educational Resources Information Center
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Problem Solving through an Optimization Problem in Geometry
ERIC Educational Resources Information Center
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
Representations in Problem Solving: A Case Study with Optimization Problems
ERIC Educational Resources Information Center
Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose
2009-01-01
Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results.
Particle swarm optimization for complex nonlinear optimization problems
NASA Astrophysics Data System (ADS)
Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos
2016-06-01
This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.
Hu, Xiaolin; Zhang, Bo
2009-04-01
In this paper, a new recurrent neural network is proposed for solving convex quadratic programming (QP) problems. Compared with existing neural networks, the proposed one features global convergence property under weak conditions, low structural complexity, and no calculation of matrix inverse. It serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems. In addition, it is found that by some variable substitution, the proposed network turns out to be an existing model for solving minimax problems. In this sense, it can be also viewed as a special case of the minimax neural network. Based on this scheme, a k-winners-take-all ( k-WTA) network with O(n) complexity is designed, which is characterized by simple structure, global convergence, and capability to deal with some ill cases. Numerical simulations are provided to validate the theoretical results obtained. More importantly, the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line.
Convex relaxations for gas expansion planning
Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; Hijazi, Hassan; Van Hentenryck, Pascal
2016-01-01
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution
Convex relaxations for gas expansion planning
Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; ...
2016-01-01
Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutionsmore » to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution« less
Optimal control problems with switching points
NASA Astrophysics Data System (ADS)
Seywald, Hans
1991-09-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
Optimization problems in the Bulgarian electoral system
NASA Astrophysics Data System (ADS)
Konstantinov, Mihail; Yanev, Kostadin; Pelova, Galina; Boneva, Juliana
2013-12-01
In this paper we consider several optimization problems for the Bulgarian bi-proportional electoral systems. Experiments with data from real elections are presented. In this way a series of previous investigations of the authors is further developed.
Combinatorial Algorithms for Optimization Problems
1991-06-01
since it is not known whether the problem has an SP algo- rithm. 1.3 Notation We use boldface notation for vectors and matrices . Suppose U is a matrix...Af the set of all 1-tuples of elements of Ai. A nxI the set of all m x n matrices whose entries are elements of Ai. We use the notation R, R+, Q, Z...X, Y E F and a > 0, 6 0 0, az +RY E F. A cone is pointed iff it does not contain a linear subspace. * The lineality space of a cone F is the largest
Variable Expansion Techniques for Decomposable Optimization Problems
2011-03-05
meration or dynamic programming. Recall the edge partition problem studied by Taskin et al. above in reference 7. (Z. Caner Taskin was supported by the...Stochastic Integer Program- ming, August 2009 August 2009. 12 2. Z. Caner Taskin, Algorithms for Solving Multi-Level Optimization Problems with Dis
Belief Propagation Algorithm for Portfolio Optimization Problems.
Shinzato, Takashi; Yasuda, Muneki
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Lee, M D; Vickers, D
2000-01-01
MacGregor and Ormerod (1996) have presented results purporting to show that human performance on visually presented traveling salesman problems, as indexed by a measure of response uncertainty, is strongly determined by the number of points in the stimulus array falling inside the convex hull, as distinct from the total number of points. It is argued that this conclusion is artifactually determined by their constrained procedure for stimulus construction, and, even if true, would be limited to arrays with fewer than around 50 points.
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Optimization Problems in Multisensor and Multitarget Tracking
2008-02-25
optimize the the mixed integer nonlinear programming problem Minimize(x,d) cr(d) + E cij(d)xij (i,j)EA Subject To: Y xij 5 1 (i = 1,...,m), (7) jEA(i...Donald Hearn, Program Manager Optimization and Discrete Mathematics Air Force Office of Scientific Research /NL 875 North Randolph Street Suite 325...Number: FA9550-04-1-0222 Recipient: Dr Donald Hearn. Program Manager Recipient*s Address: Optimization and Discrete Mathematics Air Force Office of
Quadratic optimization in ill-posed problems
NASA Astrophysics Data System (ADS)
Ben Belgacem, F.; Kaber, S.-M.
2008-10-01
Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.
Problem size, parallel architecture and optimal speedup
NASA Technical Reports Server (NTRS)
Nicol, David M.; Willard, Frank H.
1987-01-01
The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.
Contents: Introduction The dual cone of C (psi sub 1,..., psi sub n) Extreme rays The cone dual to an intersection of generalized convexity cones... Generalized difference quotients and multivariate convexity Miscellaneous applications of generalized convexity.
On convex relaxation of graph isomorphism
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-01-01
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic. PMID:25713342
Linear stochastic optimal control and estimation problem
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, F. K. B.
1980-01-01
Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.
Convex Modeling of Interactions with Strong Heredity
Haris, Asad; Witten, Daniela; Simon, Noah
2015-01-01
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set.
Semard, Gaëlle; Peulon-Agasse, Valerie; Bruchet, Auguste; Bouillon, Jean-Philippe; Cardinaël, Pascal
2010-08-13
It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater.
Optimization Problems: Duality and Multiplier Methods.
1982-02-19
provides a new computational handle on many problems in partial differential equations that can be represented as variational inequalities. Much remains...abstract entered in Block 20. If different from Report) DTIC III SUPPLEMENTARY NOTES MARO0 61M8 Nonlinear programming, stochastic programming, subgradient...following headings: (1) nonlinear programming algorithms, (2) multistage gradient analysis and nonsmooth optimization, (5) marginal values and sensitivity
Choi, Insub; Kim, JunHee; Kim, Donghyun
2016-01-01
Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called “TVDS”) is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image. PMID:27941635
Choi, Insub; Kim, JunHee; Kim, Donghyun
2016-12-08
Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.
Chan, W L; Guo, B Z
1990-03-01
A previous analysis of optimal birth control of population systems of the McKendrick type (a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control) raised 3 additional issues--free final time problem, system with phase constraints, and the mini-max control problem of a population. The free final time problem considers the minimum time problem to be a special case, but relaxes many convexity assumptions. Theorems (maximum principles) and corollaries are developed that flow from the terminology and mathematical notations set forth in the earlier article.
Solving optimization problems on computational grids.
Wright, S. J.; Mathematics and Computer Science
2001-05-01
Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms have become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software
Optimal solutions of unobservable orbit determination problems
NASA Astrophysics Data System (ADS)
Cicci, David A.; Tapley, Byron D.
1988-12-01
The method of data augmentation, in the form ofa priori covariance information on the reference solution, as a means to overcome the effects of ill-conditioning in orbit determination problems has been investigated. Specifically, for the case when ill-conditioning results from parameter non-observability and an appropriatea priori covariance is unknown, methods by which thea priori covariance is optimally chosen are presented. In problems where an inaccuratea priori covariance is provided, the optimal weighting of this data set is obtained. The feasibility of these ‘ridge-type’ solution methods is demonstrated by their application to a non-observable gravity field recovery simulation. In the simulation, both ‘ridge-type’ and conventional solutions are compared. Substantial improvement in the accuracy of the conventional solution is realized by the use of these ridge-type solution methods. The solution techniques presented in this study are applicable to observable, but ill-conditioned problems as well as the unobservable problems directly addressed. For the case of observable problems, the ridge-type solutions provide an improvement in the accuracy of the ordinary least squares solutions.
Hierarchical optimization for neutron scattering problems
Bao, Feng; Archibald, Rick; Bansal, Dipanshu; ...
2016-03-14
In this study, we present a scalable optimization method for neutron scattering problems that determines confidence regions of simulation parameters in lattice dynamics models used to fit neutron scattering data for crystalline solids. The method uses physics-based hierarchical dimension reduction in both the computational simulation domain and the parameter space. We demonstrate for silicon that after a few iterations the method converges to parameters values (interatomic force-constants) computed with density functional theory simulations.
Finite Optimal Stopping Problems: The Seller's Perspective
ERIC Educational Resources Information Center
Hemmati, Mehdi; Smith, J. Cole
2011-01-01
We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…
Hierarchical optimization for neutron scattering problems
Bao, Feng; Archibald, Rick; Bansal, Dipanshu; Delaire, Olivier
2016-06-15
We present a scalable optimization method for neutron scattering problems that determines confidence regions of simulation parameters in lattice dynamics models used to fit neutron scattering data for crystalline solids. The method uses physics-based hierarchical dimension reduction in both the computational simulation domain and the parameter space. We demonstrate for silicon that after a few iterations the method converges to parameters values (interatomic force-constants) computed with density functional theory simulations.
Interaction prediction optimization in multidisciplinary design optimization problems.
Meng, Debiao; Zhang, Xiaoling; Huang, Hong-Zhong; Wang, Zhonglai; Xu, Huanwei
2014-01-01
The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.
Multi-class DTI Segmentation: A Convex Approach.
Xie, Yuchen; Chen, Ting; Ho, Jeffrey; Vemuri, Baba C
2012-10-01
In this paper, we propose a novel variational framework for multi-class DTI segmentation based on global convex optimization. The existing variational approaches to the DTI segmentation problem have mainly used gradient-descent type optimization techniques which are slow in convergence and sensitive to the initialization. This paper on the other hand provides a new perspective on the often difficult optimization problem in DTI segmentation by providing a reasonably tight convex approximation (relaxation) of the original problem, and the relaxed convex problem can then be efficiently solved using various methods such as primal-dual type algorithms. To the best of our knowledge, such a DTI segmentation technique has never been reported in literature. We also show that a variety of tensor metrics (similarity measures) can be easily incorporated in the proposed framework. Experimental results on both synthetic and real diffusion tensor images clearly demonstrate the advantages of our method in terms of segmentation accuracy and robustness. In particular, when compared with existing state-of-the-art methods, our results demonstrate convincingly the importance as well as the benefit of using more refined and elaborated optimization method in diffusion tensor MR image segmentation.
A novel metaheuristic for continuous optimization problems: Virus optimization algorithm
NASA Astrophysics Data System (ADS)
Liang, Yun-Chia; Rodolfo Cuevas Juarez, Josue
2016-01-01
A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called 'antivirus') to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.
On domains of convergence in optimization problems
NASA Technical Reports Server (NTRS)
Diaz, Alejandro R.; Shaw, Steven S.; Pan, Jian
1990-01-01
Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.
NASA Astrophysics Data System (ADS)
Gélvez, Tatiana C.; Rueda, Hoover F.; Arguello, Henry
2016-05-01
A hyperspectral image (HSI) can be described as a set of images with spatial information across different spectral bands. Compressive spectral imaging techniques (CSI) permit to capture a 3-dimensional hyperspectral scene using 2 dimensional coded and multiplexed projections. Recovering the original scene from a very few projections can be valuable in applications such as remote sensing, video surveillance and biomedical imaging. Typically, HSI exhibit high correlations both, in the spatial and spectral dimensions. Thus, exploiting these correlations allows to accurately recover the original scene from compressed measurements. Traditional approaches exploit the sparsity of the scene when represented in a proper basis. For this purpose, an optimization problem that seeks to minimize a joint l2 - l1 norm is solved to obtain the original scene. However, there exist some HSI with an important feature which does not have been widely exploited; HSI are commonly low rank, thus only a few number of spectral signatures are presented in the image. Therefore, this paper proposes an approach to recover a simultaneous sparse and low rank hyperspectral image by exploiting both features at the same time. The proposed approach solves an optimization problem that seeks to minimize the l2-norm, penalized by the l1-norm, to force the solution to be sparse, and penalized by the nuclear norm to force the solution to be low rank. Theoretical analysis along with a set of simulations over different data sets show that simultaneously exploiting low rank and sparse structures enhances the performance of the recovery algorithm and the quality of the recovered image with an average improvement of around 3 dB in terms of the peak-signal to noise ratio (PSNR).
Maximum margin classification based on flexible convex hulls for fault diagnosis of roller bearings
NASA Astrophysics Data System (ADS)
Zeng, Ming; Yang, Yu; Zheng, Jinde; Cheng, Junsheng
2016-01-01
A maximum margin classification based on flexible convex hulls (MMC-FCH) is proposed and applied to fault diagnosis of roller bearings. In this method, the class region of each sample set is approximated by a flexible convex hull of its training samples, and then an optimal separating hyper-plane that maximizes the geometric margin between flexible convex hulls is constructed by solving a closest pair of points problem. By using the kernel trick, MMC-FCH can be extended to nonlinear cases. In addition, multi-class classification problems can be processed by constructing binary pairwise classifiers as in support vector machine (SVM). Actually, the classical SVM also can be regarded as a maximum margin classification based on convex hulls (MMC-CH), which approximates each class region with a convex hull. The convex hull is a special case of the flexible convex hull. To train a MMC-FCH classifier, time-domain and frequency-domain statistical parameters are extracted not only from raw vibration signals but also from the resulting intrinsic mode functions (IMFs) by performing empirical mode decomposition (EMD) on the raw signals, and then the distance evaluation technique (DET) is used to select salient features from the whole statistical features. The experiments on bearing datasets show that the proposed method can reliably recognize different bearing faults.
Optimal pre-scheduling of problem remappings
NASA Technical Reports Server (NTRS)
Nicol, David M.; Saltz, Joel H.
1987-01-01
A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.
Extremal Optimization for Quadratic Unconstrained Binary Problems
NASA Astrophysics Data System (ADS)
Boettcher, S.
We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.
Optimal Planning and Problem-Solving
NASA Technical Reports Server (NTRS)
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
Wang, Yong; Li, Han-Xiong; Yen, Gary G; Song, Wu
2015-04-01
In the field of evolutionary computation, there has been a growing interest in applying evolutionary algorithms to solve multimodal optimization problems (MMOPs). Due to the fact that an MMOP involves multiple optimal solutions, many niching methods have been suggested and incorporated into evolutionary algorithms for locating such optimal solutions in a single run. In this paper, we propose a novel transformation technique based on multiobjective optimization for MMOPs, called MOMMOP. MOMMOP transforms an MMOP into a multiobjective optimization problem with two conflicting objectives. After the above transformation, all the optimal solutions of an MMOP become the Pareto optimal solutions of the transformed problem. Thus, multiobjective evolutionary algorithms can be readily applied to find a set of representative Pareto optimal solutions of the transformed problem, and as a result, multiple optimal solutions of the original MMOP could also be simultaneously located in a single run. In principle, MOMMOP is an implicit niching method. In this paper, we also discuss two issues in MOMMOP and introduce two new comparison criteria. MOMMOP has been used to solve 20 multimodal benchmark test functions, after combining with nondominated sorting and differential evolution. Systematic experiments have indicated that MOMMOP outperforms a number of methods for multimodal optimization, including four recent methods at the 2013 IEEE Congress on Evolutionary Computation, four state-of-the-art single-objective optimization based methods, and two well-known multiobjective optimization based approaches.
NASA Astrophysics Data System (ADS)
Skala, Vaclav
2016-06-01
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.
First-order convex feasibility algorithms for x-ray CT
Sidky, Emil Y.; Pan Xiaochuan; Jorgensen, Jakob S.
2013-03-15
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144 Degree-Sign . The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.
An Optimal Design Problem for Submerged Bodies,
1984-01-01
problem, according to the relati, n (1.7) by (1.10) u(p) = j Y(p,q)g(q)drq- j w(q) a( drq, pEDf q n- q’ r r and, again using the jump relations one sees...by Uad: (a) Af(p) = 0, pEDf , (b) + ko = 0 on y=0 (2.3) (C) Tn- = 0 on y=-h (d) n- g on F(f) (e) 7’P C.e) - - ik 04 = o(o...surface fEUad gives rise, according to Theorem 1.1, to a potential 0=0(p;f), pEDf . The class of optimization problems that we discuss below then have the
Hybrid intelligent optimization methods for engineering problems
NASA Astrophysics Data System (ADS)
Pehlivanoglu, Yasin Volkan
The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and
Uniformly convex and strictly convex Orlicz spaces
NASA Astrophysics Data System (ADS)
Masta, Al Azhary
2016-02-01
In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.
Asymptotic solution of the optimal control problem for standard systems with delay
Zheltikov, V.P.; Efendiev, V.V.
1995-05-01
The authors consider the construction of an asymptotic solution of the terminal optimal control problem using the averaging method. The optimal process is described by the equation z = eZ (t, z, z(t-l, e, u), u), z/t=[-1,0] = {var_phi}(t), where the delay is constant and of unit magnitude, z {element_of} G is an n-dimensional vector, G {contained_in} R{sup n}, e > 0 is a small parameter, t {element_of} T {triple_bond} [0, e{sup -1}], Z {var_phi} are n-dimensional vector functions, Z is strictly convex in u for any (t, z) {element_of} T X G, u {element_of} U is the r-dimensional control vector, U is a compact set.
Convex Models of Malfunction Diagnosis in High Performance Aircraft
1989-05-01
initiated as in the open-loop mode: with one fixed non -zero control function. The time-dependent controller is actuated as soon as any of the state ... controllers ) the diagnosis algorithm is designed by solving 8 CONCLUI)ING REMARKS AND FUTURE RESEARCH 70 a sequence of linear optimization problems . For...Automatic Controller ............... 8 3.3 Numerical Demonstration of the Normal Dynamics ............ 8 4 Representing Control - Actuator Failure 16 5 Convex
LDRD Final Report: Global Optimization for Engineering Science Problems
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
Ning, Bende; Qu, Xiaobo; Guo, Di; Hu, Changwei; Chen, Zhong
2013-11-01
Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.
Parametric and Combinatorial Problems in Constrained Optimization
1993-02-28
1 ).70 0.30 5 . 49 6 i 68 :ý7 3 74 76 76 17~ 7s 1711 0301 F 70 1 86 89 90) 90) 90 91 190 89...AD-A265 595 1 (),% AGE - 3 I F’ KAi/61 MfAR Om sEB93 IIPA`ThA?4RXCTKtf COMBINATORIAL PROBLEMS IN CONSTRAINED OPTIMIZATION * ~2304/ 1 )5 AUJBREY B...POORE ~COLORADO STATE UNIVERSITY FORT COLLINS CO 80523 I SP CN SC ý N 1 -% vC iC R;N G A~ -~ S, i,’ S) 1 SCNSOR’NG M1’%C’NC (: AGENCY 4tPURT N~vBLQ
Approximating stationary points of stochastic optimization problems in Banach space
NASA Astrophysics Data System (ADS)
Balaji, Ramamurthy; Xu, Huifu
2008-11-01
In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.
Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems
NASA Astrophysics Data System (ADS)
Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.
2016-07-01
Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final cost function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Finally, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.
An adaptive multi-swarm optimizer for dynamic optimization problems.
Li, Changhe; Yang, Shengxiang; Yang, Ming
2014-01-01
The multipopulation method has been widely used to solve dynamic optimization problems (DOPs) with the aim of maintaining multiple populations on different peaks to locate and track multiple changing optima simultaneously. However, to make this approach effective for solving DOPs, two challenging issues need to be addressed. They are how to adapt the number of populations to changes and how to adaptively maintain the population diversity in a situation where changes are complicated or hard to detect or predict. Tracking the changing global optimum in dynamic environments is difficult because we cannot know when and where changes occur and what the characteristics of changes would be. Therefore, it is necessary to take these challenging issues into account in designing such adaptive algorithms. To address the issues when multipopulation methods are applied for solving DOPs, this paper proposes an adaptive multi-swarm algorithm, where the populations are enabled to be adaptive in dynamic environments without change detection. An experimental study is conducted based on the moving peaks problem to investigate the behavior of the proposed method. The performance of the proposed algorithm is also compared with a set of algorithms that are based on multipopulation methods from different research areas in the literature of evolutionary computation.
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach...combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly...the sensor problem was solved as a nonlinear MINLP problem. Specifically, the information gain obtained was maximized in order to determine the optimal
Shape optimization for contact problems based on isogeometric analysis
NASA Astrophysics Data System (ADS)
Horn, Benjamin; Ulbrich, Stefan
2016-08-01
We consider the shape optimization for mechanical connectors. To avoid the gap between the representation in CAD systems and the finite element simulation used by mathematical optimization, we choose an isogeometric approach for the solution of the contact problem within the optimization method. This leads to a shape optimization problem governed by an elastic contact problem. We handle the contact conditions using the mortar method and solve the resulting contact problem with a semismooth Newton method. The optimization problem is nonconvex and nonsmooth due to the contact conditions. To reduce the number of simulations, we use a derivative based optimization method. With the adjoint approach the design derivatives can be calculated efficiently. The resulting optimization problem is solved with a modified Bundle Trust Region algorithm.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Di Donato, Daniela; Mugnai, Dimitri
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
FRANOPP: Framework for analysis and optimization problems user's guide
NASA Technical Reports Server (NTRS)
Riley, K. M.
1981-01-01
Framework for analysis and optimization problems (FRANOPP) is a software aid for the study and solution of design (optimization) problems which provides the driving program and plotting capability for a user generated programming system. In addition to FRANOPP, the programming system also contains the optimization code CONMIN, and two user supplied codes, one for analysis and one for output. With FRANOPP the user is provided with five options for studying a design problem. Three of the options utilize the plot capability and present an indepth study of the design problem. The study can be focused on a history of the optimization process or on the interaction of variables within the design problem.
NASA Technical Reports Server (NTRS)
Tennille, Geoffrey M.; Howser, Lona M.
1993-01-01
The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.
Enhanced ant colony optimization for multiscale problems
NASA Astrophysics Data System (ADS)
Hu, Nan; Fish, Jacob
2016-03-01
The present manuscript addresses the issue of computational complexity of optimizing nonlinear composite materials and structures at multiple scales. Several solutions are detailed to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales.
Replica analysis for the duality of the portfolio optimization problem.
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
Replica analysis for the duality of the portfolio optimization problem
NASA Astrophysics Data System (ADS)
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
Optimal recombination in genetic algorithms for flowshop scheduling problems
NASA Astrophysics Data System (ADS)
Kovalenko, Julia
2016-10-01
The optimal recombination problem consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We prove NP-hardness of the optimal recombination for various variants of the flowshop scheduling problem with makespan criterion and criterion of maximum lateness. An algorithm for solving the optimal recombination problem for permutation flowshop problems is built, using enumeration of prefect matchings in a special bipartite graph. The algorithm is adopted for the classical flowshop scheduling problem and for the no-wait flowshop problem. It is shown that the optimal recombination problem for the permutation flowshop scheduling problem is solvable in polynomial time for almost all pairs of parent solutions as the number of jobs tends to infinity.
Exact optimal solution for a class of dual control problems
NASA Astrophysics Data System (ADS)
Cao, Suping; Qian, Fucai; Wang, Xiaomei
2016-07-01
This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example.
Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron
Margot, F.; Fukuda, K.; Liebling, T.
1994-12-31
We investigate the applicability of backtrack technique for solving the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is polynomial in the input size, but the vertex enumeration problem requires a backtrack algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete. Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Advances in dual algorithms and convex approximation methods
NASA Technical Reports Server (NTRS)
Smaoui, H.; Fleury, C.; Schmit, L. A.
1988-01-01
A new algorithm for solving the duals of separable convex optimization problems is presented. The algorithm is based on an active set strategy in conjunction with a variable metric method. This first order algorithm is more reliable than Newton's method used in DUAL-2 because it does not break down when the Hessian matrix becomes singular or nearly singular. A perturbation technique is introduced in order to remove the nondifferentiability of the dual function which arises when linear constraints are present in the approximate problem.
Comparison of Optimal Design Methods in Inverse Problems.
Banks, H T; Holm, Kathleen; Kappel, Franz
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].
ERIC Educational Resources Information Center
Hodge, Jonathan K.; Marshall, Emily; Patterson, Geoff
2010-01-01
Convexity-based measures of shape compactness provide an effective way to identify irregularities in congressional district boundaries. A low convexity coefficient may suggest that a district has been gerrymandered, or it may simply reflect irregularities in the corresponding state boundary. Furthermore, the distribution of population within a…
NASA Astrophysics Data System (ADS)
Cheng, Jieyu; Qiu, Wu; Yuan, Jing; Fenster, Aaron; Chiu, Bernard
2016-03-01
Registration of longitudinally acquired 3D ultrasound (US) images plays an important role in monitoring and quantifying progression/regression of carotid atherosclerosis. We introduce an image-based non-rigid registration algorithm to align the baseline 3D carotid US with longitudinal images acquired over several follow-up time points. This algorithm minimizes the sum of absolute intensity differences (SAD) under a variational optical-flow perspective within a multi-scale optimization framework to capture local and global deformations. Outer wall and lumen were segmented manually on each image, and the performance of the registration algorithm was quantified by Dice similarity coefficient (DSC) and mean absolute distance (MAD) of the outer wall and lumen surfaces after registration. In this study, images for 5 subjects were registered initially by rigid registration, followed by the proposed algorithm. Mean DSC generated by the proposed algorithm was 79:3+/-3:8% for lumen and 85:9+/-4:0% for outer wall, compared to 73:9+/-3:4% and 84:7+/-3:2% generated by rigid registration. Mean MAD of 0:46+/-0:08mm and 0:52+/-0:13mm were generated for lumen and outer wall respectively by the proposed algorithm, compared to 0:55+/-0:08mm and 0:54+/-0:11mm generated by rigid registration. The mean registration time of our method per image pair was 143+/-23s.
Splitting Methods for Convex Clustering
Chi, Eric C.; Lange, Kenneth
2016-01-01
Clustering is a fundamental problem in many scientific applications. Standard methods such as k-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of k-means and hierarchical clustering shrink cluster centroids toward one another and ensure a unique global minimizer. In this work we present two splitting methods for solving the convex clustering problem. The first is an instance of the alternating direction method of multipliers (ADMM); the second is an instance of the alternating minimization algorithm (AMA). In contrast to previously considered algorithms, our ADMM and AMA formulations provide simple and unified frameworks for solving the convex clustering problem under the previously studied norms and open the door to potentially novel norms. We demonstrate the performance of our algorithm on both simulated and real data examples. While the differences between the two algorithms appear to be minor on the surface, complexity analysis and numerical experiments show AMA to be significantly more efficient. This article has supplemental materials available online. PMID:27087770
The Role of Intuition in the Solving of Optimization Problems
ERIC Educational Resources Information Center
Malaspina, Uldarico; Font, Vicenc
2010-01-01
This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…
Alternative Solutions for Optimization Problems in Generalizability Theory.
ERIC Educational Resources Information Center
Sanders, Piet F.
1992-01-01
Presents solutions for the problem of maximizing the generalizability coefficient under a budget constraint. Shows that the Cauchy-Schwarz inequality can be applied to derive optimal continuous solutions for the number of conditions of each facet. Illustrates the formal similarity between optimization problems in survey sampling and…
Convex Accelerated Maximum Entropy Reconstruction
Worley, Bradley
2016-01-01
Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476
Liu, Ryan Wen; Shi, Lin; Yu, Simon Chun Ho; Xiong, Naixue; Wang, Defeng
2017-03-03
Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.
Liu, Ryan Wen; Shi, Lin; Yu, Simon Chun Ho; Xiong, Naixue; Wang, Defeng
2017-01-01
Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments. PMID:28273827
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
NASA Astrophysics Data System (ADS)
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Approximating convex Pareto surfaces in multiobjective radiotherapy planning
Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R.
2006-09-15
Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.
2012-08-01
relerr time relerr time 80 80 80 10 8.76e-005 4.39e-001 7.89e-005 8.64e-001 8.62e-005 8.19e-001 80 80 80 20 9.47e-005 1.26e+000 1.97e-004 1.45e+000...1.77e-004 1.21e+000 80 80 80 30 9.65e-005 2.83e+000 2.05e-004 2.13e+000 2.07e-004 1.95e+000 50 50 500 10 9.15e-005 1.27e+000 1.07e-004 1.91e+000 9.54e...completion; bold are bad or slow. Problem Setting APG-TC (prop’d) r = q APG-TC (prop’d) r = b1.25qc FaLRTC N1 N2 N3 q SR relerr time relerr time relerr time 80
Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems
NASA Technical Reports Server (NTRS)
Balling, R. J.; Wilkinson, C. A.
1997-01-01
A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.
A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations
Cui, Zengru; Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie; Wang, Xiaoliang; Duan, Xiabin
2015-01-01
This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than using second-order information of the function, thus decreasing the workload and time involved in the computation. Under suitable conditions, the algorithm converges globally to an optimal solution. Numerical results show that this algorithm can successfully solve nonsmooth unconstrained convex problems. PMID:26501775
NASA Astrophysics Data System (ADS)
Alabau-Boussouira, Fatiha
The Liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations. Extensions to infinite dimensional settings have been studied by several authors (see e.g. Haraux, 1991 [11], and Komornik and Zuazua, 1990 [17] and references therein). Results on optimal energy decay rates under general conditions of the feedback is far from being complete. The purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation. We present a general approach based on convexity arguments to establish sharp optimal or quasi-optimal upper energy decay rates for these systems, and on comparison principles based on the dissipation property, and interpolation inequalities (in the infinite dimensional case) for lower bounds of the energy. We stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi-discretized nonlinear damped vibrating PDE's. A part of this approach has been introduced in Alabau-Boussouira (2004, 2005) [1,2]. In the present paper, we identify a new, simple and explicit criteria to select a class of nonlinear feedbacks, for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in Alabau-Boussouira (2004, 2005) [1,2]. Moreover, we prove optimality of the decay rates for this class, in the finite dimensional case. This class includes a wide range of feedbacks, ranging from very weak nonlinear dissipation (exponentially decaying in a neighborhood of zero), to polynomial, or polynomial-logarithmic decaying feedbacks at the origin. In the infinite dimensional case, we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation. This principle relies on suitable interpolation inequalities. It allows us to give lower bounds for the energy of smooth initial data for the one
Solving Optimization Problems with Dynamic Geometry Software: The Airport Problem
ERIC Educational Resources Information Center
Contreras, José
2014-01-01
This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…
Solving bi-objective optimal control problems with rectangular framing
NASA Astrophysics Data System (ADS)
Wijaya, Karunia Putra; Götz, Thomas
2016-06-01
Optimization problems, e.g. arising from epidemiology models, often ask for solutions minimizing multi-criteria objective functions. In this paper we discuss a novel approach for solving bi-objective optimal control problems. The set of non-dominated points is constructed via a decreasing sequence of rectangles. Particular attention is paid to a problem with disconnected set of non-dominated points. Several examples from epidemiology are investigated and show the applicability of the method.
Neighboring extremals of dynamic optimization problems with path equality constraints
NASA Technical Reports Server (NTRS)
Lee, A. Y.
1988-01-01
Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.
Conditions on optimal support recovery in unmixing problems by means of multi-penalty regularization
NASA Astrophysics Data System (ADS)
Grasmair, Markus; Naumova, Valeriya
2016-10-01
Inspired by several real-life applications in audio processing and medical image analysis, where the quantity of interest is generated by several sources to be accurately modeled and separated, as well as by recent advances in regularization theory and optimization, we study the conditions on optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularization. We consider and analyze a regularization functional composed of a data-fidelity term, where signal and noise are additively mixed, a non-smooth, convex, sparsity promoting term, and a quadratic penalty term to model the noise. We prove not only that the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but we also demonstrate the enhanced properties of multi-penalty regularization in terms of support identification compared to sole {{\\ell }}1-minimization. We additionally confirm and support the theoretical results by extensive numerical simulations, which give a statistics of robustness of the multi-penalty regularization scheme with respect to the single-parameter counterpart. Eventually, we confirm a significant improvement in performance compared to standard {{\\ell }}1-regularization for compressive sensing problems considered in our experiments.
Singular perturbation analysis of AOTV-related trajectory optimization problems
NASA Technical Reports Server (NTRS)
Calise, Anthony J.; Bae, Gyoung H.
1990-01-01
The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality
Sensitivity analysis for electromagnetic topology optimization problems
NASA Astrophysics Data System (ADS)
Zhou, Shiwei; Li, Wei; Li, Qing
2010-06-01
This paper presents a level set based method to design the metal shape in electromagnetic field such that the incident current flow on the metal surface can be minimized or maximized. We represent the interface of the free space and conducting material (solid phase) by the zero-order contour of a higher dimensional level set function. Only the electrical component of the incident wave is considered in the current study and the distribution of the induced current flow on the metallic surface is governed by the electric field integral equation (EFIE). By minimizing or maximizing a costing function relative to the current flow, its distribution can be controlled to some extent. This method paves a new avenue to many electromagnetic applications such as antenna and metamaterial whose performance or properties are dominated by their surface current flow. The sensitivity of the objective function to the shape change, an integral formulation including both the solutions to the electric field integral equation and its adjoint equation, is obtained using a variational method and shape derivative. The advantages of the level set model lie in its flexibility of disposing complex topological changes and facilitating the mathematical expression of the electromagnetic configuration. Moreover, the level set model makes the optimization an elegant evolution process during which the volume of the metallic component keeps a constant while the free space/metal interface gradually approaching its optimal position. The effectiveness of this method is demonstrated through a self-adjoint 2D topology optimization example.
Neural networks for convex hull computation.
Leung, Y; Zhang, J S; Xu, Z B
1997-01-01
Computing convex hull is one of the central problems in various applications of computational geometry. In this paper, a convex hull computing neural network (CHCNN) is developed to solve the related problems in the N-dimensional spaces. The algorithm is based on a two-layered neural network, topologically similar to ART, with a newly developed adaptive training strategy called excited learning. The CHCNN provides a parallel online and real-time processing of data which, after training, yields two closely related approximations, one from within and one from outside, of the desired convex hull. It is shown that accuracy of the approximate convex hulls obtained is around O[K(-1)(N-1/)], where K is the number of neurons in the output layer of the CHCNN. When K is taken to be sufficiently large, the CHCNN can generate any accurate approximate convex hull. We also show that an upper bound exists such that the CHCNN will yield the precise convex hull when K is larger than or equal to this bound. A series of simulations and applications is provided to demonstrate the feasibility, effectiveness, and high efficiency of the proposed algorithm.
A Planning Problem Combining Calculus of Variations and Optimal Transport
Carlier, G. Lachapelle, A.
2011-02-15
We consider some variants of the classical optimal transport where not only one optimizes over couplings between some variables x and y but also over some control variables governing the evolutions of these variables with time. Such a situation is motivated by an assignment problem of tasks with workers whose characteristics can evolve with time (and be controlled). We distinguish between the coupled and decoupled case. The coupled case is a standard optimal transport with the value of some optimal control problem as cost. The decoupled case is more involved since it is nonlinear in the transport plan.
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
Stereotype locally convex spaces
NASA Astrophysics Data System (ADS)
Akbarov, S. S.
2000-08-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Applications of parallel global optimization to mechanics problems
NASA Astrophysics Data System (ADS)
Schutte, Jaco Francois
Global optimization of complex engineering problems, with a high number of variables and local minima, requires sophisticated algorithms with global search capabilities and high computational efficiency. With the growing availability of parallel processing, it makes sense to address these requirements by increasing the parallelism in optimization strategies. This study proposes three methods of concurrent processing. The first method entails exploiting the structure of population-based global algorithms such as the stochastic Particle Swarm Optimization (PSO) algorithm and the Genetic Algorithm (GA). As a demonstration of how such an algorithm may be adapted for concurrent processing we modify and apply the PSO to several mechanical optimization problems on a parallel processing machine. Desirable PSO algorithm features such as insensitivity to design variable scaling and modest sensitivity to algorithm parameters are demonstrated. A second approach to parallelism and improving algorithm efficiency is by utilizing multiple optimizations. With this method a budget of fitness evaluations is distributed among several independent sub-optimizations in place of a single extended optimization. Under certain conditions this strategy obtains a higher combined probability of converging to the global optimum than a single optimization which utilizes the full budget of fitness evaluations. The third and final method of parallelism addressed in this study is the use of quasiseparable decomposition, which is applied to decompose loosely coupled problems. This yields several sub-problems of lesser dimensionality which may be concurrently optimized with reduced effort.
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
A Convex Geometry-Based Blind Source Separation Method for Separating Nonnegative Sources.
Yang, Zuyuan; Xiang, Yong; Rong, Yue; Xie, Kan
2015-08-01
This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.
Comparison of optimal design methods in inverse problems
NASA Astrophysics Data System (ADS)
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Direct Multiple Shooting Optimization with Variable Problem Parameters
NASA Technical Reports Server (NTRS)
Whitley, Ryan J.; Ocampo, Cesar A.
2009-01-01
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Group Testing: Four Student Solutions to a Classic Optimization Problem
ERIC Educational Resources Information Center
Teague, Daniel
2006-01-01
This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.
Optimal control problem for impulsive systems with integral boundary conditions
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sharifov, Y. A.
2012-08-01
In the present work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
A Decision Support System for Solving Multiple Criteria Optimization Problems
ERIC Educational Resources Information Center
Filatovas, Ernestas; Kurasova, Olga
2011-01-01
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
On reductibility of degenerate optimization problems to regular operator equations
NASA Astrophysics Data System (ADS)
Bednarczuk, E. M.; Tretyakov, A. A.
2016-12-01
We present an application of the p-regularity theory to the analysis of non-regular (irregular, degenerate) nonlinear optimization problems. The p-regularity theory, also known as the p-factor analysis of nonlinear mappings, was developed during last thirty years. The p-factor analysis is based on the construction of the p-factor operator which allows us to analyze optimization problems in the degenerate case. We investigate reducibility of a non-regular optimization problem to a regular system of equations which do not depend on the objective function. As an illustration we consider applications of our results to non-regular complementarity problems of mathematical programming and to linear programming problems.
Vision-based stereo ranging as an optimal control problem
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Sridhar, B.; Chatterji, G. B.
1992-01-01
The recent interest in the use of machine vision for flight vehicle guidance is motivated by the need to automate the nap-of-the-earth flight regime of helicopters. Vision-based stereo ranging problem is cast as an optimal control problem in this paper. A quadratic performance index consisting of the integral of the error between observed image irradiances and those predicted by a Pade approximation of the correspondence hypothesis is then used to define an optimization problem. The necessary conditions for optimality yield a set of linear two-point boundary-value problems. These two-point boundary-value problems are solved in feedback form using a version of the backward sweep method. Application of the ranging algorithm is illustrated using a laboratory image pair.
The synthesis of optimal controls for linear, time-optimal problems with retarded controls.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Jacobs, M. Q.; Latina, M. R.
1971-01-01
Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
Examining the Bernstein global optimization approach to optimal power flow problem
NASA Astrophysics Data System (ADS)
Patil, Bhagyesh V.; Sampath, L. P. M. I.; Krishnan, Ashok; Ling, K. V.; Gooi, H. B.
2016-10-01
This work addresses a nonconvex optimal power flow problem (OPF). We introduce a `new approach' in the context of OPF problem based on the Bernstein polynomials. The applicability of the approach is studied on a real-world 3-bus power system. The numerical results obtained with this new approach for a 3-bus system reveal a satisfactory improvement in terms of optimality. The results are found to be competent with generic global optimization solvers BARON and COUENNE.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Chemical reaction optimization for solving shortest common supersequence problem.
Khaled Saifullah, C M; Rafiqul Islam, Md
2016-10-01
Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.
Optimal vehicle planning and the search tour problem
NASA Astrophysics Data System (ADS)
Wettergren, Thomas A.; Bays, Matthew J.
2016-05-01
We describe a problem of optimal planning for unmanned vehicles and illustrate two distinct procedures for its solution. The problem under consideration, which we refer to as the search tour problem, involves the determination of multi-stage plans for unmanned vehicles conducting search operations. These types of problems are important in situations where the searcher has varying performance in different regions throughout the domain due to environmental complexity. The ability to provide robust planning for unmanned systems under diﬃcult environmental conditions is critical for their use in search operations. The problem we consider consists of searches with variable times for each of the stages, as well as an additional degree of freedom for each stage to select from one of a finite set of operational configurations. As each combination of configuration and stage time leads to a different performance level, there is a need to determine the optimal configuration of these stages. When the complexity of constraints on total time, as well as resources expended at each stage for a given configuration, are added, the problem becomes one of non-trivial search effort allocation and numerical methods of optimization are required. We show two solution approaches for this numerical optimization problem. The first solution technique is to use a mixed-integer linear programming formulation, for which commercially available solvers can find optimal solutions in a reasonable amount of time. We use this solution as a baseline and compare against a new inner/outer optimization formulation. This inner/outer optimization compares favorably to the baseline solution, but is also amenable to adaptation as the search operation progresses. Numerical examples illustrate the utility of the approach for unmanned vehicle search planning.
One algorithm for branch and bound method for solving concave optimization problem
NASA Astrophysics Data System (ADS)
Andrianova, A. A.; Korepanova, A. A.; Halilova, I. F.
2016-11-01
The article describes the algorithm for branch and bound method for solving the concave programming problem, which is based on the idea of similarity the necessary and sufficient conditions of optimum for the original problem and for a convex programming problem with another feasible set and reverse the sign of the objective function. To find the feasible set of the equivalent convex programming problem we construct an algorithm using the idea of the branch and bound method. We formulate various branching techniques and discusses the construction of the lower objective function evaluations for the node of the decision tree. The article discusses the results of experiments of this algorithm for some famous test problems of a particular form.
Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control
NASA Astrophysics Data System (ADS)
Kamyar, Reza
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to
Sub-problem Optimization With Regression and Neural Network Approximators
NASA Technical Reports Server (NTRS)
Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.
2003-01-01
Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.
Ridzal, Danis
2007-03-01
Aristos is a Trilinos package for nonlinear continuous optimization, based on full-space sequential quadratic programming (SQP) methods. Aristos is specifically designed for the solution of large-scale constrained optimization problems in which the linearized constraint equations require iterative (i.e. inexact) linear solver techniques. Aristos' unique feature is an efficient handling of inexactness in linear system solves. Aristos currently supports the solution of equality-constrained convex and nonconvex optimization problems. It has been used successfully in the area of PDE-constrained optimization, for the solution of nonlinear optimal control, optimal design, and inverse problems.
Left ventricle segmentation in MRI via convex relaxed distribution matching.
Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben
2013-12-01
A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm
Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.
2000-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.
Optimization problems with quasi-variational inequality constraints
Outrata, J.
1994-12-31
The main aim of the contribution is to propose a numerical method for the optimization problems with parameter-dependent Quasi-Variational Inequalities (QVI) or Implicit Complementarity Problems (ICP) as side constraints. Thereby we confine ourselves to the simpler case in which the solutions of QVI (ICP) are unique (or at least locally unique) and depend on the parameter in a lipschitzian way. In the first part we state the problem and give some motivating examples coming from mechanics. The second part deals with the numerical solution of QVI (ICP) for fixed values of the parameter by a nonsmooth variant of the Newton method, which has shown a surprising effectiveness in the applications being considered. In particular, we show that the appropriate operators are semismooth and discuss the nonsingularity condition. The third part is devoted to our optimization problems which are cast in such a way that the bundle techniques from nonsmooth optimization can be applied. To compute the needed {open_quotes}subgradient{close_quotes} information, we characterize the maps, assigning to the single admissible values of the parameter the corresponding solution of the QVI, by generalized Jacobians. As a test example, the optimal covering problem from shape optimization is taken, in which the rigid obstacle is replaced by an elastic one.
Reliability optimization problems with multiple constraints under fuzziness
NASA Astrophysics Data System (ADS)
Gupta, Neha; Haseen, Sanam; Bari, Abdul
2016-06-01
In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. The imprecision in data can often be represented by triangular fuzzy numbers. In this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. We formulate a redundancy allocation problem for a hypothetical series-parallel system in which the parameters of the system are fuzzy. Two different cases are then formulated as non-linear programming problem and the fuzzy nature is defuzzified into crisp problems using three different defuzzification methods viz. ranking function, graded mean integration value and α-cut. The result of the methods is compared at the end of the manuscript using a numerical example.
A coherent Ising machine for 2000-node optimization problems
NASA Astrophysics Data System (ADS)
Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki
2016-11-01
The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
Russian Doll Search for solving Constraint Optimization problems
Verfaillie, G.; Lemaitre, M.
1996-12-31
If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminishes.
Exact solution for the optimal neuronal layout problem.
Chklovskii, Dmitri B
2004-10-01
Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.
Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.
Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860
Ant colony optimization for solving university facility layout problem
NASA Astrophysics Data System (ADS)
Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin
2013-04-01
Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).
Application of tabu search to deterministic and stochastic optimization problems
NASA Astrophysics Data System (ADS)
Gurtuna, Ozgur
During the past two decades, advances in computer science and operations research have resulted in many new optimization methods for tackling complex decision-making problems. One such method, tabu search, forms the basis of this thesis. Tabu search is a very versatile optimization heuristic that can be used for solving many different types of optimization problems. Another research area, real options, has also gained considerable momentum during the last two decades. Real options analysis is emerging as a robust and powerful method for tackling decision-making problems under uncertainty. Although the theoretical foundations of real options are well-established and significant progress has been made in the theory side, applications are lagging behind. A strong emphasis on practical applications and a multidisciplinary approach form the basic rationale of this thesis. The fundamental concepts and ideas behind tabu search and real options are investigated in order to provide a concise overview of the theory supporting both of these two fields. This theoretical overview feeds into the design and development of algorithms that are used to solve three different problems. The first problem examined is a deterministic one: finding the optimal servicing tours that minimize energy and/or duration of missions for servicing satellites around Earth's orbit. Due to the nature of the space environment, this problem is modeled as a time-dependent, moving-target optimization problem. Two solution methods are developed: an exhaustive method for smaller problem instances, and a method based on tabu search for larger ones. The second and third problems are related to decision-making under uncertainty. In the second problem, tabu search and real options are investigated together within the context of a stochastic optimization problem: option valuation. By merging tabu search and Monte Carlo simulation, a new method for studying options, Tabu Search Monte Carlo (TSMC) method, is
Adjoint optimal control problems for the RANS system
NASA Astrophysics Data System (ADS)
Attavino, A.; Cerroni, D.; Da Vià, R.; Manservisi, S.; Menghini, F.
2017-01-01
Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.
Polak, E.
1994-12-31
Unlike the situation with most other problems, the concept of a solution to an optimization problem is not unique, since it includes global solutions, local solutions, and stationary points. Earlier definitions of a consistent approximation to an optimization problem were in terms of properties that ensured that the global minimizers of the approximating problems (as well as uniformly strict local minimizers) converge only to global minimizers (local minimizers) of the original problems. Our definition of a consistent approximation addresses the properties not only of global and local solutions of the approximating problems, but also of their stationary points. Hence we always consider a pair, consisting of an optimization problem and its optimality function, (P, {theta}), with the zeros of the optimality function being the stationary points of P. We define consistency of approximating problem-optimality function pairs, (P{sub N}, {theta}{sub N}) to (P, {theta}), in terms of the epigraphical convergence of the P{sub N} to P, and the hypographical convergence of the optimality functions {theta}{sub N} to {theta}. As a companion to the characterization of consistent approximations, we will present two types of {open_quotes}diagonalization{close_quotes} techniques for using consistent approximations and {open_quotes}hot starts{close_quotes} in obtaining an approximate solution of the original problems. The first is a {open_quotes}filter{close_quotes} type technique, similar to that used in conjunction with penalty functions, the second one is an adaptive discretization technique with nicer convergence properties. We will illustrate the use of our concept of consistent approximations with examples from semi-infinite optimization, optimal control, and shape optimization.
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Comparing Extremal and Hysteretic Optimization on the Satisfiability Problem
NASA Astrophysics Data System (ADS)
Gonçalves, Bruno; Boettcher, Stefan
2006-03-01
We apply physically inspired optimization methods to the classical combinatorial Satisfiablity problem. Treating the usual boolean variables as Ising spins and each clause as a p-spin interaction we can use the pre-existing physical intuition about spin glasses and magnetic systems to find the optimal solution for this problem (the ground state energy). We compare the performance of Extremal OptimizationootnotetextPRL 23:5211, 2001 (τEO) and Hysteretic OptimizationootnotetextPRL 89:150201, 2002 (HO) and determine the parameter values that provide the best results. Comparisons with previously published results on well known benchmarksootnotetextDIMACS 35:393, 1997 are also made.
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas; Rao Zhiping Zidani, Hasnaa
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
Optimality problem of network topology in stocks market analysis
NASA Astrophysics Data System (ADS)
Djauhari, Maman Abdurachman; Gan, Siew Lee
2015-02-01
Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets' commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.
Application of clustering global optimization to thin film design problems.
Lemarchand, Fabien
2014-03-10
Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating.
Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron
2008-01-01
In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.
A Convex Approach to Fault Tolerant Control
NASA Technical Reports Server (NTRS)
Maghami, Peiman G.; Cox, David E.; Bauer, Frank (Technical Monitor)
2002-01-01
The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.
Convex weighting criteria for speaking rate estimation
Jiao, Yishan; Berisha, Visar; Tu, Ming; Liss, Julie
2015-01-01
Speaking rate estimation directly from the speech waveform is a long-standing problem in speech signal processing. In this paper, we pose the speaking rate estimation problem as that of estimating a temporal density function whose integral over a given interval yields the speaking rate within that interval. In contrast to many existing methods, we avoid the more difficult task of detecting individual phonemes within the speech signal and we avoid heuristics such as thresholding the temporal envelope to estimate the number of vowels. Rather, the proposed method aims to learn an optimal weighting function that can be directly applied to time-frequency features in a speech signal to yield a temporal density function. We propose two convex cost functions for learning the weighting functions and an adaptation strategy to customize the approach to a particular speaker using minimal training. The algorithms are evaluated on the TIMIT corpus, on a dysarthric speech corpus, and on the ICSI Switchboard spontaneous speech corpus. Results show that the proposed methods outperform three competing methods on both healthy and dysarthric speech. In addition, for spontaneous speech rate estimation, the result show a high correlation between the estimated speaking rate and ground truth values. PMID:26167516
Generalized vector calculus on convex domain
NASA Astrophysics Data System (ADS)
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
Approximated analytical solution to an Ebola optimal control problem
NASA Astrophysics Data System (ADS)
Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.
2016-11-01
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.
To the optimization problem in minority game model
NASA Astrophysics Data System (ADS)
Yanishevsky, Vasyl
2009-12-01
The article presents the research results of the optimization problem in minority game model to a gaussian approximation using replica symmetry breaking by one step (1RSB). A comparison to replica symmetry approximation (RS) and the results from literary sources received using other methods has been held.
Optimizing investment fund allocation using vehicle routing problem framework
NASA Astrophysics Data System (ADS)
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
Efficient infill sampling for unconstrained robust optimization problems
NASA Astrophysics Data System (ADS)
Rehman, Samee Ur; Langelaar, Matthijs
2016-08-01
A novel infill sampling criterion is proposed for efficient estimation of the global robust optimum of expensive computer simulation based problems. The algorithm is especially geared towards addressing problems that are affected by uncertainties in design variables and problem parameters. The method is based on constructing metamodels using Kriging and adaptively sampling the response surface via a principle of expected improvement adapted for robust optimization. Several numerical examples and an engineering case study are used to demonstrate the ability of the algorithm to estimate the global robust optimum using a limited number of expensive function evaluations.
Proposal of Evolutionary Simplex Method for Global Optimization Problem
NASA Astrophysics Data System (ADS)
Shimizu, Yoshiaki
To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.
Rees algebras, Monomial Subrings and Linear Optimization Problems
NASA Astrophysics Data System (ADS)
Dupont, Luis A.
2010-06-01
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.
Harmony search algorithm: application to the redundancy optimization problem
NASA Astrophysics Data System (ADS)
Nahas, Nabil; Thien-My, Dao
2010-09-01
The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players. Two kinds of problems are considered in testing the proposed algorithm, with the first limited to the binary series-parallel system, where the problem consists of a selection of elements and redundancy levels used to maximize the system reliability given various system-level constraints; the second problem for its part concerns the multi-state series-parallel systems with performance levels ranging from perfect operation to complete failure, and in which identical redundant elements are included in order to achieve a desirable level of availability. Numerical results for test problems from previous research are reported and compared. The results of HSA showed that this algorithm could provide very good solutions when compared to those obtained through other approaches.
Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method
NASA Astrophysics Data System (ADS)
Vasant, Pandian
2011-06-01
Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.
Boundary condition optimal control problem in lava flow modelling
NASA Astrophysics Data System (ADS)
Ismail-Zadeh, Alik; Korotkii, Alexander; Tsepelev, Igor; Kovtunov, Dmitry; Melnik, Oleg
2016-04-01
We study a problem of steady-state fluid flow with known thermal conditions (e.g., measured temperature and the heat flux at the surface of lava flow) at one segment of the model boundary and unknown conditions at its another segment. This problem belongs to a class of boundary condition optimal control problems and can be solved by data assimilation from one boundary to another using direct and adjoint models. We derive analytically the adjoint model and test the cost function and its gradient, which minimize the misfit between the known thermal condition and its model counterpart. Using optimization algorithms, we iterate between the direct and adjoint problems and determine the missing boundary condition as well as thermal and dynamic characteristics of the fluid flow. The efficiency of optimization algorithms - Polak-Ribiere conjugate gradient and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms - have been tested with the aim to get a rapid convergence to the solution of this inverse ill-posed problem. Numerical results show that temperature and velocity can be determined with a high accuracy in the case of smooth input data. A noise imposed on the input data results in a less accurate solution, but still acceptable below some noise level.
Acuña, Daniel E; Parada, Víctor
2010-07-29
Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution ("good" edges) were significantly more likely to stay than other edges ("bad" edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants "ran out of ideas." In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics.
Chance-Constrained Guidance With Non-Convex Constraints
NASA Technical Reports Server (NTRS)
Ono, Masahiro
2011-01-01
Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of
A free boundary approach to shape optimization problems
Bucur, D.; Velichkov, B.
2015-01-01
The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint. PMID:26261362
A free boundary approach to shape optimization problems.
Bucur, D; Velichkov, B
2015-09-13
The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint.
Two hybrid compaction algorithms for the layout optimization problem.
Xiao, Ren-Bin; Xu, Yi-Chun; Amos, Martyn
2007-01-01
In this paper we present two new algorithms for the layout optimization problem: this concerns the placement of circular, weighted objects inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of the container. This problem carries real practical significance in industrial applications (such as the design of satellites), as well as being of significant theoretical interest. We present two nature-inspired algorithms for this problem, the first based on simulated annealing, and the second on particle swarm optimization. We compare our algorithms with the existing best-known algorithm, and show that our approaches out-perform it in terms of both solution quality and execution time.
Ihlow, Dankmar; Kubein-Meesenburg, Dietmar; Hunze, Justus; Dathe, Henning; Planert, Jens; Schwestka-Polly, Rainer; Nägerl, Hans
2002-07-01
Radii for concave-convex vertical stripping instruments can be derived from measurements of the natural curvature morphology in the horizontal contact area of the mandibular dentition. The concave-convex adjustment of contacts in the anterior dental arch with a newly developed set of concave-convex stripping instruments should enable orthodontic crowding problems to be alleviated biomechanically.
Personality, Preventive Health Behaviour and Comparative Optimism about Health Problems.
Ingledew, D K; Brunning, S
1999-03-01
The aim was to test a model whereby personality influences preventive health behaviour which in turn influences comparative optimism about possible future health problems. Students (N 5 150) completed measures of personality (five-factor), preventive health behaviour and comparative optimism. The model was tested using structural equation modelling with observed variables. In the final model, agreeableness and conscientiousness had positive main effects and an interactive effect upon preventive health behaviour. Preventive health behaviour had a positive effect upon comparative optimism. In addition, extraversion had a direct positive effect (not mediated by preventive health behaviour) upon comparative optimism. It is speculated that agreeableness and conscientiousness combine to produce a general regard for social convention that is conducive to healthier behaviour. The effect of extraversion is explicable in terms of positive affectivity.
2016-05-01
subproblems. Our approach is expected to have wide applications in continuous dynamic games, control theory problems, and elsewhere. Mathematics...differential dynamic games, control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to...rapid numerical solutions for a non-convex Hamiltonian in high dimensions, and this method is expected to have wide applications in optimal control
Duan, Hai-Bin; Xu, Chun-Fang; Xing, Zhi-Hui
2010-02-01
In this paper, a novel hybrid Artificial Bee Colony (ABC) and Quantum Evolutionary Algorithm (QEA) is proposed for solving continuous optimization problems. ABC is adopted to increase the local search capacity as well as the randomness of the populations. In this way, the improved QEA can jump out of the premature convergence and find the optimal value. To show the performance of our proposed hybrid QEA with ABC, a number of experiments are carried out on a set of well-known Benchmark continuous optimization problems and the related results are compared with two other QEAs: the QEA with classical crossover operation, and the QEA with 2-crossover strategy. The experimental comparison results demonstrate that the proposed hybrid ABC and QEA approach is feasible and effective in solving complex continuous optimization problems.
Neural network for constrained nonsmooth optimization using Tikhonov regularization.
Qin, Sitian; Fan, Dejun; Wu, Guangxi; Zhao, Lijun
2015-03-01
This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network.
Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures
NASA Astrophysics Data System (ADS)
Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin
2012-08-01
Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.
Performance investigation of multigrid optimization for DNS-based optimal control problems
NASA Astrophysics Data System (ADS)
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
Block-oriented modeling of superstructure optimization problems
Friedman, Z; Ingalls, J; Siirola, JD; Watson, JP
2013-10-15
We present a novel software framework for modeling large-scale engineered systems as mathematical optimization problems. A key motivating feature in such systems is their hierarchical, highly structured topology. Existing mathematical optimization modeling environments do not facilitate the natural expression and manipulation of hierarchically structured systems. Rather, the modeler is forced to "flatten" the system description, hiding structure that may be exploited by solvers, and obfuscating the system that the modeling environment is attempting to represent. To correct this deficiency, we propose a Python-based "block-oriented" modeling approach for representing the discrete components within the system. Our approach is an extension of the Pyomo library for specifying mathematical optimization problems. Through the use of a modeling components library, the block-oriented approach facilitates a clean separation of system superstructure from the details of individual components. This approach also naturally lends itself to expressing design and operational decisions as disjunctive expressions over the component blocks. By expressing a mathematical optimization problem in a block-oriented manner, inherent structure (e.g., multiple scenarios) is preserved for potential exploitation by solvers. In particular, we show that block-structured mathematical optimization problems can be straightforwardly manipulated by decomposition-based multi-scenario algorithmic strategies, specifically in the context of the PySP stochastic programming library. We illustrate our block-oriented modeling approach using a case study drawn from the electricity grid operations domain: unit commitment with transmission switching and N - 1 reliability constraints. Finally, we demonstrate that the overhead associated with block-oriented modeling only minimally increases model instantiation times, and need not adversely impact solver behavior. (C) 2013 Elsevier Ltd. All rights reserved.
Multiresolution strategies for the numerical solution of optimal control problems
NASA Astrophysics Data System (ADS)
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Block clustering based on difference of convex functions (DC) programming and DC algorithms.
Le, Hoai Minh; Le Thi, Hoai An; Dinh, Tao Pham; Huynh, Van Ngai
2013-10-01
We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM.
NASA Astrophysics Data System (ADS)
Gao, Leitao; Zhao, Guangshe; Li, Guoqi; Yang, Zhaoxu
2017-03-01
The leader selection problem refers to determining a predefined number of agents as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. The original leader selection problem is formulated as a non-convex optimization problem where matrix variables are involved. By relaxing the constraints, a convex optimization model can be obtained. By introducing a chain rule of matrix differentiation, we can obtain the gradient of the cost function which consists matrix variables. We develop a "revisited projected gradient method" (RPGM) and a "probabilistic projected gradient method" (PPGM) to solve the two formulated convex and non-convex optimization problems, respectively. The convergence property of both methods is established. For convex optimization model, the global optimal solution can be achieved by RPGM, while for the original non-convex optimization model, a suboptimal solution is achieved by PPGM. Simulation results ranging from the synthetic to real-life networks are provided to show the effectiveness of RPGM and PPGM. This works will deepen the understanding of leader selection problems and enable applications in various real-life distributed control problems.
Optimization Algorithms and Equilibrium Analysis for Dynamic Resource Allocation
2012-01-31
to derive necessary and sufficient conditions for many desirable properties of a prediction market mechanism such as proper scoring, truthful...set can be non - convex or non -connected. Our method is based on approximating a quadratic social utility optimization problem (QP) and showing that...In [2], we present a convex optimization framework that unifies these seemingly unrelated models for centrally organizing contingent claims
An improved particle swarm optimization algorithm for reliability problems.
Wu, Peifeng; Gao, Liqun; Zou, Dexuan; Li, Steven
2011-01-01
An improved particle swarm optimization (IPSO) algorithm is proposed to solve reliability problems in this paper. The IPSO designs two position updating strategies: In the early iterations, each particle flies and searches according to its own best experience with a large probability; in the late iterations, each particle flies and searches according to the fling experience of the most successful particle with a large probability. In addition, the IPSO introduces a mutation operator after position updating, which can not only prevent the IPSO from trapping into the local optimum, but also enhances its space developing ability. Experimental results show that the proposed algorithm has stronger convergence and stability than the other four particle swarm optimization algorithms on solving reliability problems, and that the solutions obtained by the IPSO are better than the previously reported best-known solutions in the recent literature.
Convex recoloring as an evolutionary marker.
Frenkel, Zeev; Kiat, Yosef; Izhaki, Ido; Snir, Sagi
2017-02-01
With the availability of enormous quantities of genetic data it has become common to construct very accurate trees describing the evolutionary history of the species under study, as well as every single gene of these species. These trees allow us to examine the evolutionary compliance of given markers (characters). A marker compliant with the history of the species investigated, has undergone mutations along the species tree branches, such that every subtree of that tree exhibits a different state. Convex recoloring (CR) uses combinatorial representation to measure the adequacy of a taxonomic classifier to a given tree. Despite its biological origins, research on CR has been almost exclusively dedicated to mathematical properties of the problem, or variants of it with little, if any, relationship to taxonomy. In this work we return to the origins of CR. We put CR in a statistical framework and introduce and learn the notion of the statistical significance of a character. We apply this measure to two data sets - Passerine birds and prokaryotes, and four examples. These examples demonstrate various applications of CR, from evolutionary relatedness, through lateral evolution, to supertree construction. The above study was done with a new software that we provide, containing algorithmic improvement with a graphical output of a (optimally) recolored tree.
An optimized spectral difference scheme for CAA problems
NASA Astrophysics Data System (ADS)
Gao, Junhui; Yang, Zhigang; Li, Xiaodong
2012-05-01
In the implementation of spectral difference (SD) method, the conserved variables at the flux points are calculated from the solution points using extrapolation or interpolation schemes. The errors incurred in using extrapolation and interpolation would result in instability. On the other hand, the difference between the left and right conserved variables at the edge interface will introduce dissipation to the SD method when applying a Riemann solver to compute the flux at the element interface. In this paper, an optimization of the extrapolation and interpolation schemes for the fourth order SD method on quadrilateral element is carried out in the wavenumber space through minimizing their dispersion error over a selected band of wavenumbers. The optimized coefficients of the extrapolation and interpolation are presented. And the dispersion error of the original and optimized schemes is plotted and compared. An improvement of the dispersion error over the resolvable wavenumber range of SD method is obtained. The stability of the optimized fourth order SD scheme is analyzed. It is found that the stability of the 4th order scheme with Chebyshev-Gauss-Lobatto flux points, which is originally weakly unstable, has been improved through the optimization. The weak instability is eliminated completely if an additional second order filter is applied on selected flux points. One and two dimensional linear wave propagation analyses are carried out for the optimized scheme. It is found that in the resolvable wavenumber range the new SD scheme is less dispersive and less dissipative than the original scheme, and the new scheme is less anisotropic for 2D wave propagation. The optimized SD solver is validated with four computational aeroacoustics (CAA) workshop benchmark problems. The numerical results with optimized schemes agree much better with the analytical data than those with the original schemes.
Numerical Solution of Some Types of Fractional Optimal Control Problems
Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.
2013-01-01
We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. PMID:24385874
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Generalized Hill Climbing Algorithms For Discrete Optimization Problems
2011-07-21
the Solution of the n/m/Cmax Flowshop Problem," Computers and Operations Research, 17 (3): 243-253. Papadimitriou , C.H. and K. Steiglitz [1982...model, whereby deteriorating moves are accepted according to a general random variable. Computational results are reported that illustrate...optimal solutions. Sangiovanni-Vincentelli [1991] separates heuristic methods into two conceptual classes: a class that computes the best solution
A piecewise linear approximation scheme for hereditary optimal control problems
NASA Technical Reports Server (NTRS)
Cliff, E. M.; Burns, J. A.
1977-01-01
An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.
Overview: Applications of numerical optimization methods to helicopter design problems
NASA Technical Reports Server (NTRS)
Miura, H.
1984-01-01
There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.
Solving nonlinear equality constrained multiobjective optimization problems using neural networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques.
Computational and statistical tradeoffs via convex relaxation
Chandrasekaran, Venkat; Jordan, Michael I.
2013-01-01
Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of “algorithmic weakening,” in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data. PMID:23479655
Issues and Strategies in Solving Multidisciplinary Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya
2013-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.
Wang, Di; Kleinberg, Robert D
2009-11-28
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.
Optimal Parametric Discrete Event Control: Problem and Solution
Griffin, Christopher H
2008-01-01
We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model $G$ defined over an event alphabet $\\Sigma$ so that the plant model language $L = \\LanM(G)$ is prefix closed. We further assume the existence of a \\textit{base control structure} $M_K$, which may be either a finite state machine or a deterministic pushdown machine. If $K = \\LanM(M_K)$, we assume $K$ is prefix closed and that $K \\subseteq L$. We associate each controllable transition of $M_K$ with a binary variable $X_1,\\dots,X_n$ indicating whether the transition is enabled or not. This leads to a function $M_K(X_1,\\dots,X_n)$, that returns a new control specification depending upon the values of $X_1,\\dots,X_n$. We exhibit a branch-and-bound algorithm to solve the optimization problem $\\min_{X_1,\\dots,X_n}\\max_{w \\in K} C(w)$ such that $M_K(X_1,\\dots,X_n) \\models \\Pi$ and $\\LanM(M_K(X_1,\\dots,X_n)) \\in \\Con(L)$. Here $\\Pi$ is a set of logical assertions on the structure of $M_K(X_1,\\dots,X_n)$, and $M_K(X_1,\\dots,X_n) \\models \\Pi$ indicates that $M_K(X_1,\\dots,X_n)$ satisfies the logical assertions; and, $\\Con(L)$ is the set of controllable sublanguages of $L$.
On the degeneracy of the IMRT optimization problem.
Alber, M; Meedt, G; Nüsslin, F; Reemtsen, R
2002-11-01
One approach to the computation of photon IMRT treatment plans is the formulation of an optimization problem with an objective function that derives from an objective density. An investigation of the second-order properties of such an objective function in a neighborhood of the minimizer opens an intuitive access to many traits of this approach. A general finding is that only a small subset of the parameter space has nonzero curvature, while the objective function is entirely flat in a neighborhood of the minimizer in most directions. The dimension of the subspace of vanishing curvature serves as a measure for the degeneracy of the solution. This finding is important both for algorithm design and evaluation of the mathematical model of clinical intuition, expressed by the objective function. The structure of the subspace of great curvature is found to be imposed on the problem by conflicts between objectives of target and critical structures. These conflicts and their corresponding modes of resolution form a common trait between all reasonable treatment plans of a given case. The high degree of degeneracy makes the use of a conjugate gradient optimization algorithm particularly favorable since the number of iterations to convergence is equivalent to the number of different eigenvalues of the curvature tensor and is hence independent from the number of optimization parameters. A high level of degeneracy of the fluence profiles implies that it should be possible to stipulate further delivery-related conditions without causing severe deterioration of the dose distribution.
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification. PMID:26336509
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems.
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification.
A self-learning particle swarm optimizer for global optimization problems.
Li, Changhe; Yang, Shengxiang; Nguyen, Trung Thanh
2012-06-01
Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.
Zhang, Gexiang; Rong, Haina; Neri, Ferrante; Pérez-Jiménez, Mario J
2014-08-01
Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system.
Mathematical theory of a relaxed design problem in structural optimization
NASA Technical Reports Server (NTRS)
Kikuchi, Noboru; Suzuki, Katsuyuki
1990-01-01
Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.
Resource efficient gadgets for compiling adiabatic quantum optimization problems
NASA Astrophysics Data System (ADS)
Babbush, Ryan; O'Gorman, Bryan; Aspuru-Guzik, Alán
2013-11-01
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.
On the robust optimization to the uncertain vaccination strategy problem
Chaerani, D. Anggriani, N. Firdaniza
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
An implementable algorithm for the optimal design centering, tolerancing, and tuning problem
Polak, E.
1982-05-01
An implementable master algorithm for solving optimal design centering, tolerancing, and tuning problems is presented. This master algorithm decomposes the original nondifferentiable optimization problem into a sequence of ordinary nonlinear programming problems. The master algorithm generates sequences with accumulation points that are feasible and satisfy a new optimality condition, which is shown to be stronger than the one previously used for these problems.
Multiresolution subspace-based optimization method for inverse scattering problems.
Oliveri, Giacomo; Zhong, Yu; Chen, Xudong; Massa, Andrea
2011-10-01
This paper investigates an approach to inverse scattering problems based on the integration of the subspace-based optimization method (SOM) within a multifocusing scheme in the framework of the contrast source formulation. The scattering equations are solved by a nested three-step procedure composed of (a) an outer multiresolution loop dealing with the identification of the regions of interest within the investigation domain through an iterative information-acquisition process, (b) a spectrum analysis step devoted to the reconstruction of the deterministic components of the contrast sources, and (c) an inner optimization loop aimed at retrieving the ambiguous components of the contrast sources through a conjugate gradient minimization of a suitable objective function. A set of representative reconstruction results is discussed to provide numerical evidence of the effectiveness of the proposed algorithmic approach as well as to assess the features and potentialities of the multifocusing integration in comparison with the state-of-the-art SOM implementation.
Multigrid methods for parabolic distributed optimal control problems
NASA Astrophysics Data System (ADS)
Borzì, Alfio
2003-08-01
Multigrid schemes that solve parabolic distributed optimality systems discretized by finite differences are investigated. Accuracy properties of finite difference approximation are discussed and validated. Two multigrid methods are considered which are based on a robust relaxation technique and use two different coarsening strategies: semicoarsening and standard coarsening. The resulting multigrid algorithms show robustness with respect to changes of the value of [nu], the weight of the cost of the control, is sufficiently small. Fourier mode analysis is used to investigate the dependence of the linear twogrid convergence factor on [nu] and on the discretization parameters. Results of numerical experiments are reported that demonstrate sharpness of Fourier analysis estimates. A multigrid algorithm that solves optimal control problems with box constraints on the control is considered.
Exactly Solvable Hierarchical Optimization Problem Related to Percolation
NASA Astrophysics Data System (ADS)
Fink, Thomas M.; Ball, Robin C.
1996-04-01
We consider a sequence of elementary decisions which must be made in light of successive information learned. A key feature is that the decisions must balance the reduction of immediate cost against learning information and hence securing a wider range of future options-a conflict which motivates us to attach a value to information. We analytically derive an optimal decision policy; while each individual decision is elementary, the solution to the collective problem, which may be interpreted as a novel percolation model, exhibits a phase transition and finite size scaling.
Null testing convex optical surfaces.
Szulc, A
1997-09-01
A new test for convex optical surfaces is presented. It makes use of an auxiliary ellipsoidal mirror that is of approximately the same diameter as the convex mirror tested. The test is a null test of excellent precision. The auxiliary ellipsoid used is also tested in a null fashion, permitting good precision to be obtained.
Can linear superiorization be useful for linear optimization problems?
NASA Astrophysics Data System (ADS)
Censor, Yair
2017-04-01
Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.
Fast solvers for optimal control problems from pattern formation
NASA Astrophysics Data System (ADS)
Stoll, Martin; Pearson, John W.; Maini, Philip K.
2016-01-01
The modeling of pattern formation in biological systems using various models of reaction-diffusion type has been an active research topic for many years. We here look at a parameter identification (or PDE-constrained optimization) problem where the Schnakenberg and Gierer-Meinhardt equations, two well-known pattern formation models, form the constraints to an objective function. Our main focus is on the efficient solution of the associated nonlinear programming problems via a Lagrange-Newton scheme. In particular we focus on the fast and robust solution of the resulting large linear systems, which are of saddle point form. We illustrate this by considering several two- and three-dimensional setups for both models. Additionally, we discuss an image-driven formulation that allows us to identify parameters of the model to match an observed quantity obtained from an image.
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
On representation formulas for long run averaging optimal control problem
NASA Astrophysics Data System (ADS)
Buckdahn, R.; Quincampoix, M.; Renault, J.
2015-12-01
We investigate an optimal control problem with an averaging cost. The asymptotic behaviour of the values is a classical problem in ergodic control. To study the long run averaging we consider both Cesàro and Abel means. A main result of the paper says that there is at most one possible accumulation point - in the uniform convergence topology - of the values, when the time horizon of the Cesàro means converges to infinity or the discount factor of the Abel means converges to zero. This unique accumulation point is explicitly described by representation formulas involving probability measures on the state and control spaces. As a byproduct we obtain the existence of a limit value whenever the Cesàro or Abel values are equicontinuous. Our approach allows to generalise several results in ergodic control, and in particular it allows to cope with cases where the limit value is not constant with respect to the initial condition.
Enforcing Convexity for Improved Alignment with Constrained Local Models
Wang, Yang; Lucey, Simon; Cohn, Jeffrey F.
2010-01-01
Constrained local models (CLMs) have recently demonstrated good performance in non-rigid object alignment/tracking in comparison to leading holistic approaches (e.g., AAMs). A major problem hindering the development of CLMs further, for non-rigid object alignment/tracking, is how to jointly optimize the global warp update across all local search responses. Previous methods have either used general purpose optimizers (e.g., simplex methods) or graph based optimization techniques. Unfortunately, problems exist with both these approaches when applied to CLMs. In this paper, we propose a new approach for optimizing the global warp update in an efficient manner by enforcing convexity at each local patch response surface. Furthermore, we show that the classic Lucas-Kanade approach to gradient descent image alignment can be viewed as a special case of our proposed framework. Finally, we demonstrate that our approach receives improved performance for the task of non-rigid face alignment/tracking on the MultiPIE database and the UNBC-McMaster archive. PMID:20622926
Enhanced ant colony optimization for inventory routing problem
NASA Astrophysics Data System (ADS)
Wong, Lily; Moin, Noor Hasnah
2015-10-01
The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.
Solving the Traveling Salesman's Problem Using the African Buffalo Optimization
Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam
2016-01-01
This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive. PMID:26880872
Radio interferometric gain calibration as a complex optimization problem
NASA Astrophysics Data System (ADS)
Smirnov, O. M.; Tasse, C.
2015-05-01
Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as STEFCAL and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of COHJONES, another specialized direction-dependent calibration algorithm derived from the formalism.
Solving the Traveling Salesman's Problem Using the African Buffalo Optimization.
Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam
2016-01-01
This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.
Solving Globally-Optimal Threading Problems in ''Polynomial-Time''
Uberbacher, E.C.; Xu, D.; Xu, Y.
1999-04-12
Computational protein threading is a powerful technique for recognizing native-like folds of a protein sequence from a protein fold database. In this paper, we present an improved algorithm (over our previous work) for solving the globally-optimal threading problem, and illustrate how the computational complexity and the fold recognition accuracy of the algorithm change as the cutoff distance for pairwise interactions changes. For a given fold of m residues and M core secondary structures (or simply cores) and a protein sequence of n residues, the algorithm guarantees to find a sequence-fold alignment (threading) that is globally optimal, measured collectively by (1) the singleton match fitness, (2) pairwise interaction preference, and (3) alignment gap penalties, in O(mn + MnN{sup 1.5C-1}) time and O(mn + nN{sup C-1}) space. C, the topological complexity of a fold as we term, is a value which characterizes the overall structure of the considered pairwise interactions in the fold, which are typically determined by a specified cutoff distance between the beta carbon atoms of a pair of amino acids in the fold. C is typically a small positive integer. N represents the maximum number of possible alignments between an individual core of the fold and the protein sequence when its neighboring cores are already aligned, and its value is significantly less than n. When interacting amino acids are required to see each other, C is bounded from above by a small integer no matter how large the cutoff distance is. This indicates that the protein threading problem is polynomial-time solvable if the condition of seeing each other between interacting amino acids is sufficient for accurate fold recognition. A number of extensions have been made to our basic threading algorithm to allow finding a globally-optimal threading under various constraints, which include consistencies with (1) specified secondary structures (both cores and loops), (2) disulfide bonds, (3) active sites, etc.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
NASA Astrophysics Data System (ADS)
Kmet', Tibor; Kmet'ová, Mária
2009-09-01
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
MacGregor, J N; Ormerod, T C
2000-10-01
Lee and Vickers (2000) suggest that the results of MacGregor and Ormerod (1996), showing that the response uncertainty to traveling salesperson problems (TSPs) increases with increasing numbers of nonboundary points, may have resulted as an artifact of constraints imposed in the construction of stimuli. The fact that similar patterns of results have been obtained for our "constrained" stimuli, for a stimulus constructed under different constraints, for 13 randomly generated stimuli, and for random and patterned 48-point problems provides empirical evidence that the results are not artifactual. Lee and Vickers further suggest that, even if not artifactual, the results are in principle limited to arrays of fewer than 50 points and that, beyond this, the total number of points and number of nonboundary points are "diagnostically equivalent." This claim seems to us incorrect, since arrays of any size can be constructed that will permit experimental tests of whether problem difficulty is influenced by the number of nonboundary points, or the total number of points, or both. We present a reanalysis of our original data using hierarchical regression analysis which indicates that both factors may influence problem complexity.
An optimal iterative solver for the Stokes problem
Wathen, A.; Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
Optimality Functions in Stochastic Programming
2009-12-02
nonconvex. Non - convex stochastic optimization problems arise in such diverse applications as estimation of mixed logit models [2], engineering design...first- order necessary optimality conditions ; see for example Propositions 3.3.1 and 3.3.5 in [7] or Theorem 2.2.4 in [25]. If the evaluation of f j...procedures for validation analysis of a candidate point x ∈ IRn. Since P may be nonconvex, we focus on first-order necessary optimality conditions as
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Solving the optimal control problem of the parabolic PDEs in exploitation of oil
NASA Astrophysics Data System (ADS)
Effati, S.; Janfada, M.; Esmaeili, M.
2008-04-01
In this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem.
Applying Soft Arc Consistency to Distributed Constraint Optimization Problems
NASA Astrophysics Data System (ADS)
Matsui, Toshihiro; Silaghi, Marius C.; Hirayama, Katsutoshi; Yokoo, Makot; Matsuo, Hiroshi
The Distributed Constraint Optimization Problem (DCOP) is a fundamental framework of multi-agent systems. With DCOPs a multi-agent system is represented as a set of variables and a set of constraints/cost functions. Distributed task scheduling and distributed resource allocation can be formalized as DCOPs. In this paper, we propose an efficient method that applies directed soft arc consistency to a DCOP. In particular, we focus on DCOP solvers that employ pseudo-trees. A pseudo-tree is a graph structure for a constraint network that represents a partial ordering of variables. Some pseudo-tree-based search algorithms perform optimistic searches using explicit/implicit backtracking in parallel. However, for cost functions taking a wide range of cost values, such exact algorithms require many search iterations. Therefore additional improvements are necessary to reduce the number of search iterations. A previous study used a dynamic programming-based preprocessing technique that estimates the lower bound values of costs. However, there are opportunities for further improvements of efficiency. In addition, modifications of the search algorithm are necessary to use the estimated lower bounds. The proposed method applies soft arc consistency (soft AC) enforcement to DCOP. In the proposed method, directed soft AC is performed based on a pseudo-tree in a bottom up manner. Using the directed soft AC, the global lower bound value of cost functions is passed up to the root node of the pseudo-tree. It also totally reduces values of binary cost functions. As a result, the original problem is converted to an equivalent problem. The equivalent problem is efficiently solved using common search algorithms. Therefore, no major modifications are necessary in search algorithms. The performance of the proposed method is evaluated by experimentation. The results show that it is more efficient than previous methods.
Optimization-based interactive segmentation interface for multiregion problems.
Baxter, John S H; Rajchl, Martin; Peters, Terry M; Chen, Elvis C S
2016-04-01
Interactive segmentation is becoming of increasing interest to the medical imaging community in that it combines the positive aspects of both manual and automated segmentation. However, general-purpose tools have been lacking in terms of segmenting multiple regions simultaneously with a high degree of coupling between groups of labels. Hierarchical max-flow segmentation has taken advantage of this coupling for individual applications, but until recently, these algorithms were constrained to a particular hierarchy and could not be considered general-purpose. In a generalized form, the hierarchy for any given segmentation problem is specified in run-time, allowing different hierarchies to be quickly explored. We present an interactive segmentation interface, which uses generalized hierarchical max-flow for optimization-based multiregion segmentation guided by user-defined seeds. Applications in cardiac and neonatal brain segmentation are given as example applications of its generality.
Human opinion dynamics: An inspiration to solve complex optimization problems
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan
2013-01-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making. PMID:24141795
Convex Hull Aided Registration Method (CHARM).
Fan, Jingfan; Yang, Jian; Zhao, Yitian; Ai, Danni; Liu, Yonghuai; Wang, Ge; Wang, Yongtian
2016-08-31
Non-rigid registration finds many applications such as photogrammetry, motion tracking, model retrieval, and object recognition. In this paper we propose a novel convex hull aided registration method (CHARM) to match two point sets subject to a non-rigid transformation. Firstly, two convex hulls are extracted from the source and target respectively. Then, all points of the point sets are projected onto the reference plane through each triangular facet of the hulls. From these projections, invariant features are extracted and matched optimally. The matched feature point pairs are mapped back onto the triangular facets of the convex hulls to remove outliers that are outside any relevant triangular facet. The rigid transformation from the source to the target is robustly estimated by the random sample consensus (RANSAC) scheme through minimizing the distance between the matched feature point pairs. Finally, these feature points are utilized as the control points to achieve nonrigid deformation in the form of thin-plate spline of the entire source point set towards the target one. The experimental results based on both synthetic and real data show that the proposed algorithm outperforms several state-of-the-art ones with respect to sampling, rotational angle, and data noise. In addition, the proposed CHARM algorithm also shows higher computational efficiency compared to these methods.
Stochastic convex sparse principal component analysis.
Baytas, Inci M; Lin, Kaixiang; Wang, Fei; Jain, Anil K; Zhou, Jiayu
2016-12-01
Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.
The protein folding problem: global optimization of the force fields.
Scheraga, H A; Liwo, A; Oldziej, S; Czaplewski, C; Pillardy, J; Ripoll, D R; Vila, J A; Kazmierkiewicz, R; Saunders, J A; Arnautova, Y A; Jagielska, A; Chinchio, M; Nanias, M
2004-09-01
The evolutionary development of a theoretical approach to the protein folding problem, in our laboratory, is traced. The theoretical foundations and the development of a suitable empirical all-atom potential energy function and a global optimization search are examined. Whereas the all-atom approach has thus far succeeded for relatively small molecules and for alpha-helical proteins containing up to 46 residues, it has been necessary to develop a hierarchical approach to treat larger proteins. In the hierarchical approach to single- and multiple-chain proteins, global optimization is carried out for a simplified united residue (UNRES) description of a polypeptide chain to locate the region in which the global minimum lies. Conversion of the UNRES structures in this region to all-atom structures is followed by a local search in this region. The performance of this approach in successive CASP blind tests for predicting protein structure by an ab initio physics-based method is described. Finally, a recent attempt to compute a folding pathway is discussed.
Bailey, T; Cowles, J
1987-02-01
A new characterization of the interior of the convex hull of a finite point set is given. An inclusion test based on this characterization is, on average, almost linear in the number of points times the dimensionality.
Multiagent optimization system for solving the traveling salesman problem (TSP).
Xie, Xiao-Feng; Liu, Jiming
2009-04-01
The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP), which is a classic hard computational problem. Based on a simplified MAOS version, in which each agent manipulates on extremely limited declarative knowledge, some simple and efficient components for solving TSP, including two improving heuristics based on a generalized edge assembly recombination, are implemented. Compared with metaheuristics in adaptive memory programming, MAOS is particularly suitable for supporting cooperative search. The experimental results on two TSP benchmark data sets show that MAOS is competitive as compared with some state-of-the-art algorithms, including the Lin-Kernighan-Helsgaun, IBGLK, PHGA, etc., although MAOS does not use any explicit local search during the runtime. The contributions of MAOS components are investigated. It indicates that certain clues can be positive for making suitable selections before time-consuming computation. More importantly, it shows that the cooperative search of agents can achieve an overall good performance with a macro rule in the switch mode, which deploys certain alternate search rules with the offline performance in negative correlations. Using simple alternate rules may prevent the high difficulty of seeking an omnipotent rule that is efficient for a large data set.
Center for Shape Optimization and Material Layout
1992-01-01
that eventually participate in the optimal layout for non -self-adjoint problems . Currently, these microstructures are worked out numerically [6...the fourth order problem arising in the theory of plates. 1.2 The Fourth Order Problems Direct Approach in the Optimal Design of Plates. The state of... constraint set. In fact, the constraint set is not only nonlinear, its also non -smooth, and even non - convex . Worst of all, we do not even have an analytic
Convex polytopes and quantum separability
Holik, F.; Plastino, A.
2011-12-15
We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.
Algorithms for bilevel optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.
Yu, Xiang; Zhang, Xueqing
2017-01-01
Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle’s personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run. PMID:28192508
Robust semidefinite programming approach to the separability problem
Brandao, Fernando G.S.L.; Vianna, Reinaldo O.
2004-12-01
We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as robust semidefinite programs (RSDPs). We propose, using well known properties of RSDPs, several sufficient tests for separability of mixed states. Our results are then generalized to multipartite density operators.
Some Randomized Algorithms for Convex Quadratic Programming
Goldbach, R.
1999-01-15
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.
Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems
2003-04-01
solving optimal control problems for trajectory optimization, spacecraft attitude control, jet thruster control, missile guidance and many other... optimal control problems using a pseudospectral direct transcription method. These problems are stated here so that they may be referred to elsewhere...e.g., [7]. 2.3 Prototypical Examples Throughout this thesis two example problems are used to demonstrate various prop- erties associated with solving
Path Following in the Exact Penalty Method of Convex Programming
Zhou, Hua; Lange, Kenneth
2015-01-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044
Path Following in the Exact Penalty Method of Convex Programming.
Zhou, Hua; Lange, Kenneth
2015-07-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.
Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation
NASA Astrophysics Data System (ADS)
Kmet', Tibor; Kmet'ov, Mria
2010-09-01
A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.
Multi-label Moves for MRFs with Truncated Convex Priors
NASA Astrophysics Data System (ADS)
Veksler, Olga
Optimization with graph cuts became very popular in recent years. As more applications rely on graph cuts, different energy functions are being employed. Recent evaluation of optimization algorithms showed that the widely used swap and expansion graph cut algorithms have an excellent performance for energies where the underlying MRF has Potts prior. Potts prior corresponds to assuming that the true labeling is piecewise constant. While surprisingly useful in practice, Potts prior is clearly not appropriate in many circumstances. However for more general priors, the swap and expansion algorithms do not perform as well. Both algorithms are based on moves that give each pixel a choice of only two labels. Therefore such moves can be referred to as binary moves. Recently, range moves that act on multiple labels simultaneously were introduced. As opposed to swap and expansion, each pixel has a choice of more than two labels in a range move. Therefore we call them multi-label moves. Range moves were shown to work better for problems with truncated convex priors, which imply a piecewise smooth labeling. Inspired by range moves, we develop several different variants of multi-label moves. We evaluate them on the problem of stereo correspondence and discuss their relative merits.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Gaitsgory, Vladimir; Rossomakhine, Sergey
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
A proof of convergence of the concave-convex procedure using Zangwill's theory.
Sriperumbudur, Bharath K; Lanckriet, Gert R G
2012-06-01
The concave-convex procedure (CCCP) is an iterative algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms, including sparse support vector machines (SVMs), transductive SVMs, and sparse principal component analysis. Though CCCP is widely used in many applications, its convergence behavior has not gotten a lot of specific attention. Yuille and Rangarajan analyzed its convergence in their original paper; however, we believe the analysis is not complete. The convergence of CCCP can be derived from the convergence of the d.c. algorithm (DCA), proposed in the global optimization literature to solve general d.c. programs, whose proof relies on d.c. duality. In this note, we follow a different reasoning and show how Zangwill's global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP. This underlines Zangwill's theory as a powerful and general framework to deal with the convergence issues of iterative algorithms, after also being used to prove the convergence of algorithms like expectation-maximization and generalized alternating minimization. In this note, we provide a rigorous analysis of the convergence of CCCP by addressing two questions: When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? and when does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP.
Methods of centers and methods of feasible directions for the solution of optimal control problems.
NASA Technical Reports Server (NTRS)
Polak, E.; Mukai, H.; Pironneau, O.
1971-01-01
Demonstration of the applicability of methods of centers and of methods of feasible directions to optimal control problems. Presented experimental results show that extensions of Frank-Wolfe (1956), Zoutendijk (1960), and Pironneau-Polak (1971) algorithms for nonlinear programming problems can be quite efficient in solving optimal control problems.
Optimal Design for Parameter Estimation in EEG Problems in a 3D Multilayered Domain
2014-03-30
specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification...interrogation problem, speci cally one arising in an electroencephalography (EEG) problem, of nding optimal number and locations for sensors for source identi
Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm
NASA Astrophysics Data System (ADS)
Kania, Adhe; Sidarto, Kuntjoro Adji
2016-02-01
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
Test Problems for Large-Scale Multiobjective and Many-Objective Optimization.
Cheng, Ran; Jin, Yaochu; Olhofer, Markus; Sendhoff, Bernhard
2016-08-26
The interests in multiobjective and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multiobjective and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multiobjective and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms (EAs) for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multiobjective and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multiobjective and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and nonuniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multiobjective and many-objective EAs are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.
NASA Astrophysics Data System (ADS)
Gao, Qian
For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is
A maximum principle for smooth optimal impulsive control problems with multipoint state constraints
NASA Astrophysics Data System (ADS)
Dykhta, V. A.; Samsonyuk, O. N.
2009-06-01
A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A necessary optimality condition is formulated in the form of a smooth maximum principle; thorough comments are given, a short proof is presented, and examples are discussed.
Pontriagin's maximum principle in problems of the optimization of diffraction electronic instruments
NASA Astrophysics Data System (ADS)
Tarasov, M. M.; Tretiakov, O. A.; Shestopalov, V. P.; Shmatko, A. A.
The possibilities afforded by the use of Pontriagin's maximum principle in electronics are demonstrated by applying it to an optimization problem of practical interest. The problem consists of optimizing the parameters of a maximum-efficiency diffraction oscillator for a given power output over a specified frequency range for a selected electron gun. As an example, the optimization problem is solved numerically for an oscillator with a Gaussian distribution of the high-frequency field envelope in an open resonator.
On the application of deterministic optimization methods to stochastic control problems
NASA Technical Reports Server (NTRS)
Kramer, L. C.; Athans, M.
1974-01-01
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
A numerical method for solving optimal control problems using state parametrization
NASA Astrophysics Data System (ADS)
Mehne, H.; Borzabadi, A.
2006-06-01
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
Revisiting the method of characteristics via a convex hull algorithm
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Mercier, Jean-Marc
2015-10-01
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we propose a novel numerical algorithm-the convex hull algorithm (CHA)-which allows us to compute both entropy dissipative solutions (satisfying all entropy inequalities) and entropy conservative (or multi-valued) solutions. From the multi-valued solutions determined by the method of characteristics, our algorithm "extracts" the entropy dissipative solutions, even after the formation of shocks. It applies to both convex and non-convex flux/Hamiltonians. We demonstrate the relevance of the proposed method with a variety of numerical tests, including conservation laws in one or two spatial dimensions and problem arising in fluid dynamics.
On optimal solutions of the constrained ℓ 0 regularization and its penalty problem
NASA Astrophysics Data System (ADS)
Zhang, Na; Li, Qia
2017-02-01
The constrained {{\\ell}0} regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the connections between global minimizers of the constrained {{\\ell}0} problem and its penalty problem have never been studied in a systematic way. This work provides a comprehensive investigation on optimal solutions of these two problems and their connections. We give detailed descriptions of optimal solutions of the two problems, including existence, stability with respect to the parameter, cardinality and strictness. In particular, we find that the optimal solution set of the penalty problem is piecewise constant with respect to the penalty parameter. Then we analyze in-depth the relationship between optimal solutions of the two problems. It is shown that, in the noisy case the least square penalty problem probably has no common optimal solutions with the constrained {{\\ell}0} problem for any penalty parameter. Under a mild condition on the penalty function, we establish that the penalty problem has the same optimal solution set as the constrained {{\\ell}0} problem when the penalty parameter is sufficiently large. Based on the conditions, we further propose exact penalty problems for the constrained {{\\ell}0} problem. Finally, we present a numerical example to illustrate our main theoretical results.
Active Batch Selection via Convex Relaxations with Guaranteed Solution Bounds.
Chakraborty, Shayok; Balasubramanian, Vineeth; Sun, Qian; Panchanathan, Sethuraman; Ye, Jieping
2015-10-01
Active learning techniques have gained popularity to reduce human effort in labeling data instances for inducing a classifier. When faced with large amounts of unlabeled data, such algorithms automatically identify the exemplar instances for manual annotation. More recently, there have been attempts towards a batch mode form of active learning, where a batch of data points is simultaneously selected from an unlabeled set. In this paper, we propose two novel batch mode active learning (BMAL) algorithms: BatchRank and BatchRand. We first formulate the batch selection task as an NP-hard optimization problem; we then propose two convex relaxations, one based on linear programming and the other based on semi-definite programming to solve the batch selection problem. Finally, a deterministic bound is derived on the solution quality for the first relaxation and a probabilistic bound for the second. To the best of our knowledge, this is the first research effort to derive mathematical guarantees on the solution quality of the BMAL problem. Our extensive empirical studies on 15 binary, multi-class and multi-label challenging datasets corroborate that the proposed algorithms perform at par with the state-of-the-art techniques, deliver high quality solutions and are robust to real-world issues like label noise and class imbalance.
NASA Astrophysics Data System (ADS)
Schütze, Niels; Wöhling, Thomas; de Play, Michael
2010-05-01
Some real-world optimization problems in water resources have a high-dimensional space of decision variables and more than one objective function. In this work, we compare three general-purpose, multi-objective simulation optimization algorithms, namely NSGA-II, AMALGAM, and CMA-ES-MO when solving three real case Multi-objective Optimization Problems (MOPs): (i) a high-dimensional soil hydraulic parameter estimation problem; (ii) a multipurpose multi-reservoir operation problem; and (iii) a scheduling problem in deficit irrigation. We analyze the behaviour of the three algorithms on these test problems considering their formulations ranging from 40 up to 120 decision variables and 2 to 4 objectives. The computational effort required by each algorithm in order to reach the true Pareto front is also analyzed.
Approximation of the optimal-time problem for controlled differential inclusions
Otakulov, S.
1995-01-01
One of the common methods for numerical solution of optimal control problems constructs an approximating sequence of discrete control problems. The approximation method is also attractive because it can be used as an effective tool for analyzing optimality conditions and other topics in optimization theory. In this paper, we consider the approximation of optimal-time problems for controlled differential inclusions. The sequence of approximating problems is constructed using a finite-difference scheme, i.e., the differential inclusions are replaced with difference inclusions.
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
A global optimization algorithm for simulation-based problems via the extended DIRECT scheme
NASA Astrophysics Data System (ADS)
Liu, Haitao; Xu, Shengli; Wang, Xiaofang; Wu, Junnan; Song, Yang
2015-11-01
This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.
An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.
Islam, Md Monjurul; Singh, Hemant Kumar; Ray, Tapabrata; Sinha, Ankur
2016-11-07
Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.
Solving Two-Level Optimization Problems with Applications to Robust Design and Energy Markets
2011-01-01
made up of only robust points otherwise the term is ill-defined. There is also a global counterpart as defined below. Definition 2.6: Globally ...optimal robust: For a robust optimization problem, a globally optimal robust solution x*, is a robust point such that x* is optimal ( xxfxf...Since this dissertation‟s approach is based on gradient-based methods, a globally optimal robust solution can never be guaranteed for the complete
Detection of Convexity and Concavity in Context
ERIC Educational Resources Information Center
Bertamini, Marco
2008-01-01
Sensitivity to shape changes was measured, in particular detection of convexity and concavity changes. The available data are contradictory. The author used a change detection task and simple polygons to systematically manipulate convexity/concavity. Performance was high for detecting a change of sign (a new concave vertex along a convex contour…
Revisiting separation properties of convex fuzzy sets
Technology Transfer Automated Retrieval System (TEKTRAN)
Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...
A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo
1996-01-01
A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.
A Generalized Orienteering Problem for Optimal Search and Interdiction Planning
2013-09-01
exploit this resource trade-o through a specialized branch -and- bound algorithm that relies on partial path relaxation problems , which often yield tight...computing inexpensive upper bounds based on a binary knapsack problem . This is possible because the arc lengths and rewards are xed values...algorithm that relies on partial path relaxation problems , which often yield tight bounds and lead to substantial pruning in the enumeration tree. We
Newton's method for large bound-constrained optimization problems.
Lin, C.-J.; More, J. J.; Mathematics and Computer Science
1999-01-01
We analyze a trust region version of Newton's method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large bound-constrained problems.
Convexity preserving C2 rational quadratic trigonometric spline
NASA Astrophysics Data System (ADS)
Dube, Mridula; Tiwari, Preeti
2012-09-01
A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.
A faster optimization method based on support vector regression for aerodynamic problems
NASA Astrophysics Data System (ADS)
Yang, Xixiang; Zhang, Weihua
2013-09-01
In this paper, a new strategy for optimal design of complex aerodynamic configuration with a reasonable low computational effort is proposed. In order to solve the formulated aerodynamic optimization problem with heavy computation complexity, two steps are taken: (1) a sequential approximation method based on support vector regression (SVR) and hybrid cross validation strategy, is proposed to predict aerodynamic coefficients, and thus approximates the objective function and constraint conditions of the originally formulated optimization problem with given limited sample points; (2) a sequential optimization algorithm is proposed to ensure the obtained optimal solution by solving the approximation optimization problem in step (1) is very close to the optimal solution of the originally formulated optimization problem. In the end, we adopt a complex aerodynamic design problem, that is optimal aerodynamic design of a flight vehicle with grid fins, to demonstrate our proposed optimization methods, and numerical results show that better results can be obtained with a significantly lower computational effort than using classical optimization techniques.
Non-convex entropies for conservation laws with involutions.
Dafermos, Constantine M
2013-12-28
The paper discusses systems of conservation laws endowed with involutions and contingent entropies. Under the assumption that the contingent entropy function is convex merely in the direction of a cone in state space, associated with the involution, it is shown that the Cauchy problem is locally well posed in the class of classical solutions, and that classical solutions are unique and stable even within the broader class of weak solutions that satisfy an entropy inequality. This is on a par with the classical theory of solutions to hyperbolic systems of conservation laws endowed with a convex entropy. The equations of elastodynamics provide the prototypical example for the above setting.
Improving the efficiency of solving discrete optimization problems: The case of VRP
NASA Astrophysics Data System (ADS)
Belov, A.; Slastnikov, S.
2016-02-01
Paper is devoted constructing efficient metaheuristics algorithms for discrete optimization problems. Particularly, we consider vehicle routing problem applying original ant colony optimization method to solve it. Besides, some parts of algorithm are separated for parallel computing. Some experimental results are performed to compare the efficiency of these methods.
Optimization in First Semester Calculus: A Look at a Classic Problem
ERIC Educational Resources Information Center
LaRue, Renee; Infante, Nicole Engelke
2015-01-01
Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…
Solving Continuous-Time Optimal-Control Problems with a Spreadsheet.
ERIC Educational Resources Information Center
Naevdal, Eric
2003-01-01
Explains how optimal control problems can be solved with a spreadsheet, such as Microsoft Excel. Suggests the method can be used by students, teachers, and researchers as a tool to find numerical solutions for optimal control problems. Provides several examples that range from simple to advanced. (JEH)
Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem
NASA Astrophysics Data System (ADS)
Dai, Min; Yi, Fahuai
This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.
A novel geometric approach to binary classification based on scaled convex hulls.
Liu, Zhenbing; Liu, J G; Pan, Chao; Wang, Guoyou
2009-07-01
Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time.
Optimal birth control of age-dependent competitive species III. Overtaking problem
NASA Astrophysics Data System (ADS)
He, Ze-Rong; Cheng, Ji-Shu; Zhang, Chun-Guo
2008-01-01
A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.
Optimizing material properties of composite plates for sound transmission problem
NASA Astrophysics Data System (ADS)
Tsai, Yu-Ting; Pawar, S. J.; Huang, Jin H.
2015-01-01
To calculate the specific transmission loss (TL) of a composite plate, the conjugate gradient optimization method is utilized to estimate and optimize material properties of the composite plate in this study. For an n-layer composite plate, a nonlinear dynamic stiffness matrix based on the thick plate theory is formulated. To avoid huge computational efforts due to the combination of different composite material plates, a transfer matrix approach is proposed to restrict the dynamic stiffness matrix of the composite plate to a 4×4 matrix. Moreover, the transfer matrix approach has also been used to simplify the complexity of the objective function gradient for the optimization method. Numerical simulations are performed to validate the present algorithm by comparing the TL of the optimal composite plate with that of the original plate. Small number of iterations required during convergence tests illustrates the efficiency of the optimization method. The results indicate that an excellent estimation for the composite plate can be obtained for the desired sound transmission.
One-class classification based on the convex hull for bearing fault detection
NASA Astrophysics Data System (ADS)
Zeng, Ming; Yang, Yu; Luo, Songrong; Cheng, Junsheng
2016-12-01
Originating from a nearest point problem, a novel method called one-class classification based on the convex hull (OCCCH) is proposed for one-class classification problems. The basic goal of OCCCH is to find the nearest point to the origin from the reduced convex hull of training samples. A generalized Gilbert algorithm is proposed to solve the nearest point problem. It is a geometric algorithm with high computational efficiency. OCCCH has two different forms, i.e., OCCCH-1 and OCCCH-2. The relationships among OCCCH-1, OCCCH-2 and one-class support vector machine (OCSVM) are investigated theoretically. The classification accuracy and the computational efficiency of the three methods are compared through the experiments conducted on several benchmark datasets. Experimental results show that OCCCH (including OCCCH-1 and OCCCH-2) using the generalized Gilbert algorithm performs more efficiently than OCSVM using the well-known sequential minimal optimization (SMO) algorithm; at the same time, OCCCH-2 can always obtain comparable classification accuracies to OCSVM. Finally, these methods are applied to the monitoring model constructions for bearing fault detection. Compared with OCCCH-2 and OCSVM, OCCCH-1 can significantly decrease the false alarm ratio while detecting the bearing fault successfully.
Solving the optimal attention allocation problem in manual control
NASA Technical Reports Server (NTRS)
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
Cano, Emilio L.; Moguerza, Javier M.; Alonso-Ayuso, Antonio
2015-01-01
Optimization instances relate to the input and output data stemming from optimization problems in general. Typically, an optimization problem consists of an objective function to be optimized (either minimized or maximized) and a set of constraints. Thus, objective and constraints are jointly a set of equations in the optimization model. Such equations are a combination of decision variables and known parameters, which are usually related to a set domain. When this combination is a linear combination, we are facing a classical Linear Programming (LP) problem. An optimization instance is related to an optimization model. We refer to that model as the Symbolic Model Specification (SMS) containing all the sets, variables, and parameters symbols and relations. Thus, a whole instance is composed by the SMS, the elements in each set, the data values for all the parameters, and, eventually, the optimal decisions resulting from the optimization solution. This data article contains several optimization instances from a real-world optimization problem relating to investment planning on energy efficient technologies at the building level. PMID:26693515
Cano, Emilio L; Moguerza, Javier M; Alonso-Ayuso, Antonio
2015-12-01
Optimization instances relate to the input and output data stemming from optimization problems in general. Typically, an optimization problem consists of an objective function to be optimized (either minimized or maximized) and a set of constraints. Thus, objective and constraints are jointly a set of equations in the optimization model. Such equations are a combination of decision variables and known parameters, which are usually related to a set domain. When this combination is a linear combination, we are facing a classical Linear Programming (LP) problem. An optimization instance is related to an optimization model. We refer to that model as the Symbolic Model Specification (SMS) containing all the sets, variables, and parameters symbols and relations. Thus, a whole instance is composed by the SMS, the elements in each set, the data values for all the parameters, and, eventually, the optimal decisions resulting from the optimization solution. This data article contains several optimization instances from a real-world optimization problem relating to investment planning on energy efficient technologies at the building level.
2015-01-01
Optimization and 2) hybrid metaheuristics algorithm comprising a combination of ACO, Genetic Algorithm (GA) and heuristics are proposed and tested on...Optimization, Split Delivery Vehicle Routing Problem, Genetic Algorithm 1. Introduction The Vehicle Routing Problem (VRP) is a prominent problem in the areas...several heuristic methods have been applied to solve the SDVRP, such as a construction heuristic (Wilck and Cavalier, 2012a), a genetic algorithm (Wilck
Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation
NASA Technical Reports Server (NTRS)
Mook, D. J.; Lew, Jiann-Shiun
1991-01-01
Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.
Optimization technique for problems with an inequality constraint
NASA Technical Reports Server (NTRS)
Russell, K. J.
1972-01-01
General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.
Erem, Burak; van Dam, Peter M.; Brooks, Dana H.
2014-01-01
Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a non-convex, non-linear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second. PMID:24710159
Some Marginalist Intuition Concerning the Optimal Commodity Tax Problem
ERIC Educational Resources Information Center
Brett, Craig
2006-01-01
The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…
Application of the method of maximum entropy in the mean to classification problems
NASA Astrophysics Data System (ADS)
Gzyl, Henryk; ter Horst, Enrique; Molina, German
2015-11-01
In this note we propose an application of the method of maximum entropy in the mean to solve a class of inverse problems comprising classification problems and feasibility problems appearing in optimization. Such problems may be thought of as linear inverse problems with convex constraints imposed on the solution as well as on the data. The method of maximum entropy in the mean proves to be a very useful tool to deal with this type of problems.
Shi, Huan-Nan; Zhang, Jing; Ma, Qing-Hua
2016-01-01
In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.
An optimization method for the problems of thermal cloaking of material bodies
NASA Astrophysics Data System (ADS)
Alekseev, G. V.; Levin, V. A.
2016-11-01
Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.
Discrete bat algorithm for optimal problem of permutation flow shop scheduling.
Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang
2014-01-01
A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem.
Convex Diffraction Grating Imaging Spectrometer
NASA Technical Reports Server (NTRS)
Chrisp, Michael P. (Inventor)
1999-01-01
A 1:1 Offner mirror system for imaging off-axis objects is modified by replacing a concave spherical primary mirror that is concentric with a convex secondary mirror with two concave spherical mirrors M1 and M2 of the same or different radii positioned with their respective distances d1 and d2 from a concentric convex spherical diffraction grating having its grooves parallel to the entrance slit of the spectrometer which replaces the convex secondary mirror. By adjusting their distances d1 and d2 and their respective angles of reflection alpha and beta, defined as the respective angles between their incident and reflected rays, all aberrations are corrected without the need to increase the spectrometer size for a given entrance slit size to reduce astigmatism, thus allowing the imaging spectrometer volume to be less for a given application than would be possible with conventional imaging spectrometers and still give excellent spatial and spectral imaging of the slit image spectra over the focal plane.
Singular optimal control and the identically non-regular problem in the calculus of variations
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.
1985-01-01
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
NASA Astrophysics Data System (ADS)
Antipin, A. S.; Artem'eva, L. A.; Vasil'ev, F. P.
2017-01-01
An optimal control problem formulated as a system of linear ordinary differential equations with boundary conditions implicitly specified as a solution to a finite-dimensional minimization problem is considered. An extragradient method for solving this problem is proposed, and its convergence is studied.
Compiling Planning into Quantum Optimization Problems: A Comparative Study
2015-06-07
become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum ...devices designed to run only this type of quantum algorithm . Other types of quan- tum algorithms are known that take on quite a different form, and are
IPDO-2007 - Inverse Problems, Design and Optimization Symposium
2007-12-01
TRANSDUCER 107 INVERSE APPROACHES TO DRYING OF SLICED FOODS 509 108 INVERSE APPROACHES IN IMPROVEMENT OF AIR POLUTION PLUME DISPERSION MODELS FOR... Air Force Office of Scientific Research Optimization & Discrete Mathematics / NL Suite 325, Room 3112 875 Randolph Street Arlington, VA 22203-1768 11...G.S., Orlande, H.R.B., Tanaka, M. and Colaco, M.J.), Miami Beach, FL, April 16-18, 2007. 5. Inverse Approaches in Improvement of Air Pollution Plume
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
NASA Astrophysics Data System (ADS)
Piñeros, William D.; Baldea, Michael; Truskett, Thomas M.
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.
Piñeros, William D; Baldea, Michael; Truskett, Thomas M
2016-08-07
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Optimal control problems with switching points. Ph.D. Thesis, 1990 Final Report
NASA Technical Reports Server (NTRS)
Seywald, Hans
1991-01-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION
Wang, Lan; Kim, Yongdai; Li, Runze
2014-01-01
We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis. PMID:24948843
Individual Differences in Optimization Problem Solving: Reconciling Conflicting Results
ERIC Educational Resources Information Center
Chronicle, Edward P.; MacGregor, James N.; Lee, Michael; Ormerod, Thomas C.; Hughes, Peter
2008-01-01
Results on human performance on the Traveling Salesman Problem (TSP) from different laboratories show high consistency. However, one exception is in the area of individual differences. While one research group has consistently failed to find systematic individual differences across instances of TSPs (Chronicle, MacGregor and Ormerod), another…
A Bayesian observer replicates convexity context effects in figure-ground perception.
Goldreich, Daniel; Peterson, Mary A
2012-01-01
Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.
Discrete-time entropy formulation of optimal and adaptive control problems
NASA Technical Reports Server (NTRS)
Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.
1992-01-01
The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.
A Convex Atomic-Norm Approach to Multiple Sequence Alignment and Motif Discovery
Yen, Ian E. H.; Lin, Xin; Zhang, Jiong; Ravikumar, Pradeep; Dhillon, Inderjit S.
2016-01-01
Multiple Sequence Alignment and Motif Discovery, known as NP-hard problems, are two fundamental tasks in Bioinformatics. Existing approaches to these two problems are based on either local search methods such as Expectation Maximization (EM), Gibbs Sampling or greedy heuristic methods. In this work, we develop a convex relaxation approach to both problems based on the recent concept of atomic norm and develop a new algorithm, termed Greedy Direction Method of Multiplier, for solving the convex relaxation with two convex atomic constraints. Experiments show that our convex relaxation approach produces solutions of higher quality than those standard tools widely-used in Bioinformatics community on the Multiple Sequence Alignment and Motif Discovery problems. PMID:27559428
A robust optimization methodology for preliminary aircraft design
NASA Astrophysics Data System (ADS)
Prigent, S.; Maréchal, P.; Rondepierre, A.; Druot, T.; Belleville, M.
2016-05-01
This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.
NASA Astrophysics Data System (ADS)
Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu
2015-12-01
For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.
Qin, Sitian; Le, Xinyi; Wang, Jun
2016-08-19
This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.
An algorithm for LQ optimal actuator location
NASA Astrophysics Data System (ADS)
Darivandi, Neda; Morris, Kirsten; Khajepour, Amir
2013-03-01
The locations of the control hardware are typically a design variable in controller design for distributed parameter systems. In order to obtain the most efficient control system, the locations of control hardware as well as the feedback gain should be optimized. These optimization problems are generally non-convex. In addition, the models for these systems typically have a large number of degrees of freedom. Consequently, existing optimization schemes for optimal actuator placement may be inaccurate or computationally impractical. In this paper, the feedback control is chosen to be an optimal linear quadratic regulator. The optimal actuator location problem is reformulated as a convex optimization problem. A subgradient-based optimization scheme which leads to the global solution of the problem is used to optimize actuator locations. The optimization algorithm is applied to optimize the placement of piezoelectric actuators in vibration control of flexible structures. This method is compared with a genetic algorithm, and is observed to be faster and more accurate. Experiments are performed to verify the efficacy of optimal actuator placement.
The solution of singular optimal control problems using direct collocation and nonlinear programming
NASA Astrophysics Data System (ADS)
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
An optimal control problem for ovine brucellosis with culling.
Nannyonga, B; Mwanga, G G; Luboobi, L S
2015-01-01
A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2-11. Available at http://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.
Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem
Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi
2013-01-01
Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429
A VLSI optimal constructive algorithm for classification problems
Beiu, V.; Draghici, S.; Sethi, I.K.
1997-10-01
If neural networks are to be used on a large scale, they have to be implemented in hardware. However, the cost of the hardware implementation is critically sensitive to factors like the precision used for the weights, the total number of bits of information and the maximum fan-in used in the network. This paper presents a version of the Constraint Based Decomposition training algorithm which is able to produce networks using limited precision integer weights and units with limited fan-in. The algorithm is tested on the 2-spiral problem and the results are compared with other existing algorithms.
Probabilistic Analysis of Combinatorial Optimization Problems on Hypergraph Matchings
2012-02-01
by (31) satisfty �k` D dX rD1 Nık; Or .`/ D d 1; whence dH .1; O/ D n.d 1/. 3.2 Expected distance to global optimum Many heuristic solution...are necessary to reach a global optimum from a current feasible solution, or, in other words, the 16 Hamming distance from the given solution to the...identically distributed (iid) random variables with a continuous distribution, then problem (3) has a unique global minimum (since the costs of all feasible
NASA Astrophysics Data System (ADS)
Afshar, M. H.
2007-04-01
This paper exploits the unique feature of the Ant Colony Optimization Algorithm (ACOA), namely incremental solution building mechanism, to develop partially constraint ACO algorithms for the solution of optimization problems with explicit constraints. The method is based on the provision of a tabu list for each ant at each decision point of the problem so that some constraints of the problem are satisfied. The application of the method to the problem of storm water network design is formulated and presented. The network nodes are considered as the decision points and the nodal elevations of the network are used as the decision variables of the optimization problem. Two partially constrained ACO algorithms are formulated and applied to a benchmark example of storm water network design and the results are compared with those of the original unconstrained algorithm and existing methods. In the first algorithm the positive slope constraints are satisfied explicitly and the rest are satisfied by using the penalty method while in the second one the satisfaction of constraints regarding the maximum ratio of flow depth to the diameter are also achieved explicitly via the tabu list. The method is shown to be very effective and efficient in locating the optimal solutions and in terms of the convergence characteristics of the resulting ACO algorithms. The proposed algorithms are also shown to be relatively insensitive to the initial colony used compared to the original algorithm. Furthermore, the method proves itself capable of finding an optimal or near-optimal solution, independent of the discretisation level and the size of the colony used.
A distributed approach to the OPF problem
NASA Astrophysics Data System (ADS)
Erseghe, Tomaso
2015-12-01
This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.
Optimizing Constrained Single Period Problem under Random Fuzzy Demand
NASA Astrophysics Data System (ADS)
Taleizadeh, Ata Allah; Shavandi, Hassan; Riazi, Afshin
2008-09-01
In this paper, we consider the multi-product multi-constraint newsboy problem with random fuzzy demands and total discount. The demand of the products is often stochastic in the real word but the estimation of the parameters of distribution function may be done by fuzzy manner. So an appropriate option to modeling the demand of products is using the random fuzzy variable. The objective function of proposed model is to maximize the expected profit of newsboy. We consider the constraints such as warehouse space and restriction on quantity order for products, and restriction on budget. We also consider the batch size for products order. Finally we introduce a random fuzzy multi-product multi-constraint newsboy problem (RFM-PM-CNP) and it is changed to a multi-objective mixed integer nonlinear programming model. Furthermore, a hybrid intelligent algorithm based on genetic algorithm, Pareto and TOPSIS is presented for the developed model. Finally an illustrative example is presented to show the performance of the developed model and algorithm.
Use of Convexity in Ostomy Care
Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel
2017-01-01
Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174
A dual method for optimal control problems with initial and final boundary constraints.
NASA Technical Reports Server (NTRS)
Pironneau, O.; Polak, E.
1973-01-01
This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.
Necessary and sufficient conditions under which an H2 optimal control problem has a unique solution
NASA Technical Reports Server (NTRS)
Chen, Ben M.; Saberi, Ali
1993-01-01
A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.
On the application of deterministic optimization methods to stochastic control problems.
NASA Technical Reports Server (NTRS)
Kramer, L. C.; Athans, M.
1972-01-01
A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.
On unified modeling, theory, and method for solving multi-scale global optimization problems
NASA Astrophysics Data System (ADS)
Gao, David Yang
2016-10-01
A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.
Baxter, John S H; Inoue, Jiro; Drangova, Maria; Peters, Terry M
2016-10-01
Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of "shape complexes," which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems.
Analysis and formulation of a class of complex dynamic optimization problems
NASA Astrophysics Data System (ADS)
Kameswaran, Shivakumar
The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs. The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits. The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization. As an effort to extend the applicability of the direct
Qin, Sitian; Yang, Xiudong; Xue, Xiaoping; Song, Jiahui
2016-05-24
Pseudoconvex optimization problem, as an important nonconvex optimization problem, plays an important role in scientific and engineering applications. In this paper, a recurrent one-layer neural network is proposed for solving the pseudoconvex optimization problem with equality and inequality constraints. It is proved that from any initial state, the state of the proposed neural network reaches the feasible region in finite time and stays there thereafter. It is also proved that the state of the proposed neural network is convergent to an optimal solution of the related problem. Compared with the related existing recurrent neural networks for the pseudoconvex optimization problems, the proposed neural network in this paper does not need the penalty parameters and has a better convergence. Meanwhile, the proposed neural network is used to solve three nonsmooth optimization problems, and we make some detailed comparisons with the known related conclusions. In the end, some numerical examples are provided to illustrate the effectiveness of the performance of the proposed neural network.
Multigrid one shot methods for optimal control problems: Infinite dimensional control
NASA Technical Reports Server (NTRS)
Arian, Eyal; Taasan, Shlomo
1994-01-01
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.
Inclusion of known integrals in the optimal trajectory problem
NASA Technical Reports Server (NTRS)
Burns, R. E.
1974-01-01
The classical problem of determination of the rocket trajectory which minimizes mass expenditure during motion between two points in the field of a single gravitating body is analyzed. The known integrals of the system are incorporated into the adjoint equations resulting in a reduction from a seventh-order adjoint system to a third-order adjoint system. The first case which is treated in that of planar motion under specific end conditions. In this case a regularization of the recently derived equations is achieved. The general three-dimensional case is also reduced from a seventh-order adjoint system to a third-order adjoint system. In this case a regularization has not been found.
Optimization of location routing inventory problem with transshipment
NASA Astrophysics Data System (ADS)
Ghani, Nor Edayu Abd; Shariff, S. Sarifah Radiah; Zahari, Siti Meriam
2015-05-01
Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.
Terekhov, Alexander V; Zatsiorsky, Vladimir M
2011-02-01
One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423-453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.
Zatsiorsky, Vladimir M.
2011-01-01
One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907
Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.
Flat tori in three-dimensional space and convex integration.
Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris
2012-05-08
It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C(1) and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.
Online support vector machine based on convex hull vertices selection.
Wang, Di; Qiao, Hong; Zhang, Bo; Wang, Min
2013-04-01
The support vector machine (SVM) method, as a promising classification technique, has been widely used in various fields due to its high efficiency. However, SVM cannot effectively solve online classification problems since, when a new sample is misclassified, the classifier has to be retrained with all training samples plus the new sample, which is time consuming. According to the geometric characteristics of SVM, in this paper we propose an online SVM classifier called VS-OSVM, which is based on convex hull vertices selection within each class. The VS-OSVM algorithm has two steps: 1) the samples selection process, in which a small number of skeleton samples constituting an approximate convex hull in each class of the current training samples are selected and 2) the online updating process, in which the classifier is updated with newly arriving samples and the selected skeleton samples. From the theoretical point of view, the first d+1 (d is the dimension of the input samples) selected samples are proved to be vertices of the convex hull. This guarantees that the selected samples in our approach keep the greatest amount of information of the convex hull. From the application point of view, the new algorithm can update the classifier without reducing its classification performance. Experimental results on benchmark data sets have shown the validity and effectiveness of the VS-OSVM algorithm.
Flat tori in three-dimensional space and convex integration
Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris
2012-01-01
It is well-known that the curvature tensor is an isometric invariant of C2 Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C1. This unexpected flexibility has many paradoxical consequences, one of them is the existence of C1 isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash’s results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C1 fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C1 and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations. PMID:22523238
Shinzato, Takashi
2016-12-01
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.
Ant Colony Optimization with Memory and Its Application to Traveling Salesman Problem
NASA Astrophysics Data System (ADS)
Wang, Rong-Long; Zhao, Li-Qing; Zhou, Xiao-Fan
Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.
Can we predict the difficulty of optimization problems without solving them?
NASA Astrophysics Data System (ADS)
Katzgraber, Helmut G.; Fang, Chao; Lawrence, Richard; Melchert, Oliver; Munoz-Bauza, Humberto; Ochoa, Andrew J.; Wang, Wenlong; Zhu, Zheng
Surprisingly often. Based on previous results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass where it was demonstrated that autocorrelation times are directly correlated with the roughness of the free-energy landscape, we show that a generalized spin-glass order parameter can be used as a proxy to the computational difficulty of various paradigmatic optimization problems. Our results are illustrated with different optimization algorithms, as well as optimization problems. Furthermore, we show numerical evidence that the order-parameter distribution does mirror salient features in the free-energy landscape of complex systems for moderate system sizes.
NASA Astrophysics Data System (ADS)
Shinzato, Takashi
2016-12-01
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.
A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1991-01-01
The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
A New Large-Scale Global Optimization Method and Its Application to Lennard-Jones Problems
1992-11-01
stochastic methods. Computational results on Lennard - Jones problems show that the new method is considerably more successful than any other method that...our method does not find as good a solution as has been found by the best special purpose methods for Lennard - Jones problems. This illustrates the inherent difficulty of large scale global optimization.
A well-posed optimal spectral element approximation for the Stokes problem
NASA Technical Reports Server (NTRS)
Maday, Y.; Patera, A. T.; Ronquist, E. M.
1987-01-01
A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.
Selecting radiotherapy dose distributions by means of constrained optimization problems.
Alfonso, J C L; Buttazzo, G; García-Archilla, B; Herrero, M A; Núñez, L
2014-05-01
The main steps in planning radiotherapy consist in selecting for any patient diagnosed with a solid tumor (i) a prescribed radiation dose on the tumor, (ii) bounds on the radiation side effects on nearby organs at risk and (iii) a fractionation scheme specifying the number and frequency of therapeutic sessions during treatment. The goal of any radiotherapy treatment is to deliver on the tumor a radiation dose as close as possible to that selected in (i), while at the same time conforming to the constraints prescribed in (ii). To this day, considerable uncertainties remain concerning the best manner in which such issues should be addressed. In particular, the choice of a prescription radiation dose is mostly based on clinical experience accumulated on the particular type of tumor considered, without any direct reference to quantitative radiobiological assessment. Interestingly, mathematical models for the effect of radiation on biological matter have existed for quite some time, and are widely acknowledged by clinicians. However, the difficulty to obtain accurate in vivo measurements of the radiobiological parameters involved has severely restricted their direct application in current clinical practice.In this work, we first propose a mathematical model to select radiation dose distributions as solutions (minimizers) of suitable variational problems, under the assumption that key radiobiological parameters for tumors and organs at risk involved are known. Second, by analyzing the dependence of such solutions on the parameters involved, we then discuss the manner in which the use of those minimizers can improve current decision-making processes to select clinical dosimetries when (as is generally the case) only partial information on model radiosensitivity parameters is available. A comparison of the proposed radiation dose distributions with those actually delivered in a number of clinical cases strongly suggests that solutions of our mathematical model can be
Optimization-based additive decomposition of weakly coercive problems with applications
Bochev, Pavel B.; Ridzal, Denis
2016-01-27
In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem, our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.
Optimization in first semester calculus: a look at a classic problem
NASA Astrophysics Data System (ADS)
LaRue, Renee; Engelke Infante, Nicole
2015-10-01
Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional problem-solving framework. We are particularly interested in students' evoked concept images for the mathematical concepts that play a role in the construction of the function whose minimum is needed. Data analysis revealed several gaps in students' understanding of the optimization process. We highlight the mathematical concepts that play a role in these gaps, focusing on variables, function notation, function composition, properties of rectangles and the relationships between them, the role of the optimizing function, and the graphical representation of the function.
Optimization-based additive decomposition of weakly coercive problems with applications
Bochev, Pavel B.; Ridzal, Denis
2016-01-27
In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
NASA Astrophysics Data System (ADS)
Ghosh, Pradipto
The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development
L^1 -optimality conditions for the circular restricted three-body problem
NASA Astrophysics Data System (ADS)
Chen, Zheng
2016-06-01
In this paper, the L^1 -minimization for the translational motion of a spacecraft in the circular restricted three-body problem (CRTBP) is considered. Necessary conditions are derived by using the Pontryagin Maximum Principle (PMP), revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, recalling the existence of the Fuller phenomenon according to the theories developed in (Marchal in J Optim Theory Appl 11(5):441-486, 1973; Zelikin and Borisov in Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering. Birkhäuser, Basal 1994; in J Math Sci 114(3):1227-1344, 2003). The sufficient optimality conditions for the L^1 -minimization problem with fixed endpoints have been developed in (Chen et al. in SIAM J Control Optim 54(3):1245-1265, 2016). In the current paper, we establish second-order conditions for optimal control problems with more general final conditions defined by a smooth submanifold target. In addition, the numerical implementation to check these optimality conditions is given. Finally, approximating the Earth-Moon-Spacecraft system by the CRTBP, an L^1 -minimization trajectory for the translational motion of a spacecraft is computed by combining a shooting method with a continuation method in (Caillau et al. in Celest Mech Dyn Astron 114:137-150, 2012; Caillau and Daoud in SIAM J Control Optim 50(6):3178-3202, 2012). The local optimality of the computed trajectory is asserted thanks to the second-order optimality conditions developed.
Application of the steepest ascent optimization method to a reentry trajectory problem
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
The direct optimization method is presented in detail. Nominal values of the control variables are input parameters. Perturbations are introduced into the control variables and the resulting first order predictions of changes in the payoff, and constraint functions are then determined. Through a sequence of prescribed cycles, a trajectory is eventually obtained which is reasonably close to the optimum. The method is successfully applied to an Apollo three-dimensional reentry problem. The study of this Apollo application problem has resulted in the development of a highly flexible computer program that can be modified to consider other trajectory optimization problems.
NASA Astrophysics Data System (ADS)
Shinzato, Takashi
2017-02-01
In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is intuitive that the minimal investment risk for the problem with an investment concentration constraint can be larger than that without the constraint (that is, with only the budget constraint). Moreover, a numerical experiment shows the effectiveness of our proposed analysis. In contrast, the standard operations research approach failed to identify accurately the minimal investment risk of the portfolio optimization problem.
A numerical study of hybrid optimization methods for the molecular conformation problems
Meza, J.C.; Martinez, M.L.
1993-05-01
An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules depends on the accurate determination of their three-dimensional structure or conformation. Under the assumption that molecules will settle into a configuration for which their energy is at a minimum, this design problem can be formulated as a global optimization problem. The solution of the molecular conformation problem can then be obtained, at least in principle, through any number of optimization algorithms. Unfortunately, it can easily be shown that there exist a large number of local minima for most molecules which makes this an extremely difficult problem for any standard optimization method. In this study, we present results for various optimization algorithms applied to a molecular conformation problem. We include results for genetic algorithms, simulated annealing, direct search methods, and several gradient methods. The major result of this study is that none of these standard methods can be used in isolation to efficiently generate minimum energy configurations. We propose instead several hybrid methods that combine properties of several local optimization algorithms. These hybrid methods have yielded better results on representative test problems than single methods.
Finite element solution of optimal control problems with state-control inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1992-01-01
It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.
Lazarov, R D; Pasciak, J E; Schoberl, J; Vassilevski, P S
2001-08-08
We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.
A Transformation Approach to Optimal Control Problems with Bounded State Variables
NASA Technical Reports Server (NTRS)
Hanafy, Lawrence Hanafy
1971-01-01
A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.
NASA Astrophysics Data System (ADS)
Cutbill, Adam; Wang, G. Gary
2016-01-01
Constraints are necessary in optimization problems to steer optimization algorithms away from solutions which are not feasible or practical. However, redundant constraints are often added, which needlessly complicate the problem's description. This article introduces a probabilistic method to identify redundant inequality constraints for black-box optimization problems. The method uses Jaccard similarity to find item groups where the occurrence of a single item implies the occurrence of all other items in the group. The remaining groups are then mined with association analysis. Furthermore, unnecessary constraints are classified as redundant owing to co-occurrence, implication or covering. These classifications are presented as rules (in readable text), to indicate the relationships among constraints. The algorithm is applied to mathematical problems and to the engineering design of a pressure vessel. It was found that the rules are informative and correct, based on the available samples. Limitations of the proposed methods are also discussed.
Tabu search method with random moves for globally optimal design
NASA Astrophysics Data System (ADS)
Hu, Nanfang
1992-09-01
Optimum engineering design problems are usually formulated as non-convex optimization problems of continuous variables. Because of the absence of convexity structure, they can have multiple minima, and global optimization becomes difficult. Traditional methods of optimization, such as penalty methods, can often be trapped at a local optimum. The tabu search method with random moves to solve approximately these problems is introduced. Its reliability and efficiency are examined with the help of standard test functions. By the analysis of the implementations, it is seen that this method is easy to use, and no derivative information is necessary. It outperforms the random search method and composite genetic algorithm. In particular, it is applied to minimum weight design examples of a three-bar truss, coil springs, a Z-section and a channel section. For the channel section, the optimal design using the tabu search method with random moves saved 26.14 percent over the weight of the SUMT method.
NASA Technical Reports Server (NTRS)
Tapia, R. A.; Vanrooy, D. L.
1976-01-01
A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.
NASA Astrophysics Data System (ADS)
Cottrill, Gerald C.
A hybrid numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized Polynomial Chaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. TheGPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved by applying standard differential equation methods. The resulting set of deterministic solutions is used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. Optimal control problems are especially challenging to solve since they often include path constraints, bounded controls, boundary conditions, and require solutions that minimize a cost functional. Adding random parameters can make these problems even more challenging. The hybrid algorithm presented in this dissertation is the first time the GPM and gPC algorithms have been combined to solve optimal control problems with random parameters. Using the GPM in the gPC construct provides minimum cost deterministic solutions used in stochastic computations that meet path, control, and boundary constraints, thus extending current gPC methods to be applicable to stochastic optimal control problems. The hybrid GPM-gPC algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a trajectory optimization problem simulating an aircraft flying through a threat field where exact locations of the threats are unknown. The results show that the expected value, variance, and covariance statistics of the polynomial output function approximations of the state, control, cost, and terminal time variables agree with Monte-Carlo simulation
A convex penalty for switching control of partial differential equations
Clason, Christian; Rund, Armin; Kunisch, Karl; ...
2016-01-19
A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.
ERIC Educational Resources Information Center
Swanson, David
2011-01-01
We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.
1990-01-01
to Convex Bodies, Geometriae Dedicata 2" (1973) 225-248. 10. H. Guggenheimer, "The Analytic Geometry of the Unsymmetric Minkowski Plane," Lecture...Mathematics, Vol. 58, No. 2, 1975. 19. E. Lutwak, "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80
A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.
Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo
2017-01-20
Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.
Formulation and numerical solution of finite-level quantum optimal control problems
NASA Astrophysics Data System (ADS)
Borzi`, A.; Salomon, J.; Volkwein, S.
2008-06-01
Optimal control of finite-level quantum systems is investigated, and iterative solution schemes for the optimization of a control representing laser pulses are developed. The purpose of this external field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources or population suppression of certain states, are accounted for through an appropriately chosen cost functional. First-order necessary optimality conditions and second-order sufficient optimality conditions are investigated. For solving the optimal control problems, a cascadic non-linear conjugate gradient scheme and a monotonic scheme are discussed. Results of numerical experiments with a representative finite-level quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches.
Constrained iterations for blind deconvolution and convexity issues
NASA Astrophysics Data System (ADS)
Spaletta, Giulia; Caucci, Luca
2006-12-01
The need for image restoration arises in many applications of various scientific disciplines, such as medicine and astronomy and, in general, whenever an unknown image must be recovered from blurred and noisy data [M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Philadelphia, PA, USA, 1998]. The algorithm studied in this work restores the image without the knowledge of the blur, using little a priori information and a blind inverse filter iteration. It represents a variation of the methods proposed in Kundur and Hatzinakos [A novel blind deconvolution scheme for image restoration using recursive filtering, IEEE Trans. Signal Process. 46(2) (1998) 375-390] and Ng et al. [Regularization of RIF blind image deconvolution, IEEE Trans. Image Process. 9(6) (2000) 1130-1134]. The problem of interest here is an inverse one, that cannot be solved by simple filtering since it is ill-posed. The imaging system is assumed to be linear and space-invariant: this allows a simplified relationship between unknown and observed images, described by a point spread function modeling the distortion. The blurring, though, makes the restoration ill-conditioned: regularization is therefore also needed, obtained by adding constraints to the formulation. The restoration is modeled as a constrained minimization: particular attention is given here to the analysis of the objective function and on establishing whether or not it is a convex function, whose minima can be located by classic optimization techniques and descent methods. Numerical examples are applied to simulated data and to real data derived from various applications. Comparison with the behavior of methods [D. Kundur, D. Hatzinakos, A novel blind deconvolution scheme for image restoration using recursive filtering, IEEE Trans. Signal Process. 46(2) (1998) 375-390] and [M. Ng, R.J. Plemmons, S. Qiao, Regularization of RIF Blind Image Deconvolution, IEEE Trans. Image Process. 9
The Sizing and Optimization Language, (SOL): Computer language for design problems
NASA Technical Reports Server (NTRS)
Lucas, Stephen H.; Scotti, Stephen J.
1988-01-01
The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.
Constrained spacecraft reorientation using mixed integer convex programming
NASA Astrophysics Data System (ADS)
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
NASA Astrophysics Data System (ADS)
Farhi, Edward; Gosset, David; Hen, Itay; Sandvik, A. W.; Shor, Peter; Young, A. P.; Zamponi, Francesco
2012-11-01
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular max-cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.
Using a derivative-free optimization method for multiple solutions of inverse transport problems
Armstrong, Jerawan C.; Favorite, Jeffrey A.
2016-01-14
Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.
Using a derivative-free optimization method for multiple solutions of inverse transport problems
Armstrong, Jerawan C.; Favorite, Jeffrey A.
2016-01-14
Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less
A penalty method for PDE-constrained optimization in inverse problems
NASA Astrophysics Data System (ADS)
van Leeuwen, T.; Herrmann, F. J.
2016-01-01
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate.
Mixtures, Generalized Convexity and Balayages.
1986-06-01
A I X) Bk dX(x 11Xi)1 (Sufficiency) Let f c C (K). Then, by LeIn 4.3, Corollary 4.5, Lera 4.6 and the definition of v , I fdv - ldv0 , hfdvo hf( ) 1k...denote the mixed model. hen the models, F., 9 c e , arise from a family of densities (f: 0 e e) with respect to a q-finite measure m, f- fe dX will...said to be a dilation of another d distribution F, written G > F, if I cdF cdG for all convex c .) Shaked showed that fx - f e has two sign changes and
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-03-16
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency.
Feng, Ruibin; Leung, Chi-Sing; Constantinides, Anthony G; Zeng, Wen-Jun
2016-07-27
The major limitation of the Lagrange programming neural network (LPNN) approach is that the objective function and the constraints should be twice differentiable. Since sparse approximation involves nondifferentiable functions, the original LPNN approach is not suitable for recovering sparse signals. This paper proposes a new formulation of the LPNN approach based on the concept of the locally competitive algorithm (LCA). Unlike the classical LCA approach which is able to solve unconstrained optimization problems only, the proposed LPNN approach is able to solve the constrained optimization problems. Two problems in sparse approximation are considered. They are basis pursuit (BP) and constrained BP denoise (CBPDN). We propose two LPNN models, namely, BP-LPNN and CBPDN-LPNN, to solve these two problems. For these two models, we show that the equilibrium points of the models are the optimal solutions of the two problems, and that the optimal solutions of the two problems are the equilibrium points of the two models. Besides, the equilibrium points are stable. Simulations are carried out to verify the effectiveness of these two LPNN models.
A Convex Formulation for Magnetic Particle Imaging X-Space Reconstruction.
Konkle, Justin J; Goodwill, Patrick W; Hensley, Daniel W; Orendorff, Ryan D; Lustig, Michael; Conolly, Steven M
2015-01-01
Magnetic Particle Imaging (mpi) is an emerging imaging modality with exceptional promise for clinical applications in rapid angiography, cell therapy tracking, cancer imaging, and inflammation imaging. Recent publications have demonstrated quantitative mpi across rat sized fields of view with x-space reconstruction methods. Critical to any medical imaging technology is the reliability and accuracy of image reconstruction. Because the average value of the mpi signal is lost during direct-feedthrough signal filtering, mpi reconstruction algorithms must recover this zero-frequency value. Prior x-space mpi recovery techniques were limited to 1d approaches which could introduce artifacts when reconstructing a 3d image. In this paper, we formulate x-space reconstruction as a 3d convex optimization problem and apply robust a priori knowledge of image smoothness and non-negativity to reduce non-physical banding and haze artifacts. We conclude with a discussion of the powerful extensibility of the presented formulation for future applications.
Network Lasso: Clustering and Optimization in Large Graphs
Hallac, David; Leskovec, Jure; Boyd, Stephen
2016-01-01
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the network lasso, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular — binary classification, predicting housing prices, and event detection in time series data — comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems. PMID:27398260
NASA Technical Reports Server (NTRS)
Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.
1989-01-01
A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.
The optimal control frequency response problem in manual control. [of manned aircraft systems
NASA Technical Reports Server (NTRS)
Harrington, W. W.
1977-01-01
An optimal control frequency response problem is defined within the context of the optimal pilot model. The problem is designed to specify pilot model control frequencies reflective of important aircraft system properties, such as control feel system dynamics, airframe dynamics, and gust environment, as well as man machine properties, such as task and attention allocation. This is accomplished by determining a bounded set of control frequencies which minimize the total control cost. The bounds are given by zero and the neuromuscular control frequency response for each control actuator. This approach is fully adaptive, i.e., does not depend upon user entered estimates. An algorithm is developed to solve this optimal control frequency response problem. The algorithm is then applied to an attitude hold task for a bare airframe fighter aircraft case with interesting dynamic properties.
New optimization problems arising in modelling of 2D-crystal lattices
NASA Astrophysics Data System (ADS)
Evtushenko, Yury; Lurie, Sergey; Posypkin, Mikhail
2016-10-01
The paper considers the problem of finding the structure of a fragment of two-dimensional crystal lattice with the minimal energy. Atoms in a lattice reside on parallel lines (layers). The interatomic distances are the same within one layer but can differ for distinct layers. The energy of the piece of material is computed using so-called potential functions. We used Lennard-Jones, Morse and Tersoff potentials. The proposed formulation can serve as a scalable complex non-smooth optimization test. The paper evaluates various optimization techniques for the problem under consideration, compares their performances and draws the conclusion about the best choice of optimization methods for the problem under test. As a result we were able to locate minima meaningful from the physical point of view, e.g. reproducing graphene lattice.
NASA Astrophysics Data System (ADS)
Tsuchiya, Kazuo; Nishiyama, Takehiro; Tsujita, Katsuyoshi
2001-02-01
We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance.
NASA Astrophysics Data System (ADS)
Ibrahim, Ireen Munira; Liong, Choong-Yeun; Bakar, Sakhinah Abu; Ahmad, Norazura; Najmuddin, Ahmad Farid
2015-12-01
The Emergency Department (ED) is a very complex system with limited resources to support increase in demand. ED services are considered as good quality if they can meet the patient's expectation. Long waiting times and length of stay is always the main problem faced by the management. The management of ED should give greater emphasis on their capacity of resources in order to increase the quality of services, which conforms to patient satisfaction. This paper is a review of work in progress of a study being conducted in a government hospital in Selangor, Malaysia. This paper proposed a simulation optimization model framework which is used to study ED operations and problems as well as to find an optimal solution to the problems. The integration of simulation and optimization is hoped can assist management in decision making process regarding their resource capacity planning in order to improve current and future ED operations.
Vortex generator design for aircraft inlet distortion as a numerical optimization problem
NASA Technical Reports Server (NTRS)
Anderson, Bernhard H.; Levy, Ralph
1991-01-01
Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.
Using the PORS Problems to Examine Evolutionary Optimization of Multiscale Systems
Reinhart, Zachary; Molian, Vaelan; Bryden, Kenneth
2013-01-01
Nearly all systems of practical interest are composed of parts assembled across multiple scales. For example, an agrodynamic system is composed of flora and fauna on one scale; soil types, slope, and water runoff on another scale; and management practice and yield on another scale. Or consider an advanced coal-fired power plant: combustion and pollutant formation occurs on one scale, the plant components on another scale, and the overall performance of the power system is measured on another. In spite of this, there are few practical tools for the optimization of multiscale systems. This paper examines multiscale optimization of systems composed of discrete elements using the plus-one-recall-store (PORS) problem as a test case or study problem for multiscale systems. From this study, it is found that by recognizing the constraints and patterns present in discrete multiscale systems, the solution time can be significantly reduced and much more complex problems can be optimized.
The solution of the optimization problem of small energy complexes using linear programming methods
NASA Astrophysics Data System (ADS)
Ivanin, O. A.; Director, L. B.
2016-11-01
Linear programming methods were used for solving the optimization problem of schemes and operation modes of distributed generation energy complexes. Applicability conditions of simplex method, applied to energy complexes, including installations of renewable energy (solar, wind), diesel-generators and energy storage, considered. The analysis of decomposition algorithms for various schemes of energy complexes was made. The results of optimization calculations for energy complexes, operated autonomously and as a part of distribution grid, are presented.
Stochastic learning via optimizing the variational inequalities.
Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei
2014-10-01
A wide variety of learning problems can be posed in the framework of convex optimization. Many efficient algorithms have been developed based on solving the induced optimization problems. However, there exists a gap between the theoretically unbeatable convergence rate and the practically efficient learning speed. In this paper, we use the variational inequality (VI) convergence to describe the learning speed. To this end, we avoid the hard concept of regret in online learning and directly discuss the stochastic learning algorithms. We first cast the regularized learning problem as a VI. Then, we present a stochastic version of alternating direction method of multipliers (ADMMs) to solve the induced VI. We define a new VI-criterion to measure the convergence of stochastic algorithms. While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems cannot be better than O(1/√t), the proposed stochastic ADMM (SADMM) is proved to have an O(1/t) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness. The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly. The experiments demonstrate that SADMM has almost the same performance as the state-of-the-art stochastic learning algorithms but its O(1/t) VI-convergence rate is capable of tightly characterizing the real learning speed.
Optimization problems in natural gas transportation systems. A state-of-the-art review
Ríos-Mercado, Roger Z.; Borraz-Sánchez, Conrado
2015-03-24
Our paper provides a review on the most relevant research works conducted to solve natural gas transportation problems via pipeline systems. The literature reveals three major groups of gas pipeline systems, namely gathering, transmission, and distribution systems. In this work, we aim at presenting a detailed discussion of the efforts made in optimizing natural gas transmission lines.There is certainly a vast amount of research done over the past few years on many decision-making problems in the natural gas industry and, specifically, in pipeline network optimization. In this work, we present a state-of-the-art survey focusing on specific categories that include short-term basis storage (line-packing problems), gas quality satisfaction (pooling problems), and compressor station modeling (fuel cost minimization problems). We also discuss both steady-state and transient optimization models highlighting the modeling aspects and the most relevant solution approaches known to date. Although the literature on natural gas transmission system problems is quite extensive, this is, to the best of our knowledge, the first comprehensive review or survey covering this specific research area on natural gas transmission from an operations research perspective. Furthermore, this paper includes a discussion of the most important and promising research areas in this field. Hence, our paper can serve as a useful tool to gain insight into the evolution of the many real-life applications and most recent advances in solution methodologies arising from this exciting and challenging research area of decision-making problems.
An Optimization-Based Method for Feature Ranking in Nonlinear Regression Problems.
Bravi, Luca; Piccialli, Veronica; Sciandrone, Marco
2016-02-03
In this paper, we consider the feature ranking problem, where, given a set of training instances, the task is to associate a score with the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to reduce the high dimensionality of real-world data. We focus on regression problems by assuming that the process underlying the generated data can be approximated by a continuous function (for instance, a feedforward neural network). We formally state the notion of relevance of a feature by introducing a minimum zero-norm inversion problem of a neural network, which is a nonsmooth, constrained optimization problem. We employ a concave approximation of the zero-norm function, and we define a smooth, global optimization problem to be solved in order to assess the relevance of the features. We present the new feature ranking method based on the solution of instances of the global optimization problem depending on the available training data. Computational experiments on both artificial and real data sets are performed, and point out that the proposed feature ranking method is a valid alternative to existing methods in terms of effectiveness. The obtained results also show that the method is costly in terms of CPU time, and this may be a limitation in the solution of large-dimensional problems.
NASA Astrophysics Data System (ADS)
Igeta, Hideki; Hasegawa, Mikio
Chaotic dynamics have been effectively applied to improve various heuristic algorithms for combinatorial optimization problems in many studies. Currently, the most used chaotic optimization scheme is to drive heuristic solution search algorithms applicable to large-scale problems by chaotic neurodynamics including the tabu effect of the tabu search. Alternatively, meta-heuristic algorithms are used for combinatorial optimization by combining a neighboring solution search algorithm, such as tabu, gradient, or other search method, with a global search algorithm, such as genetic algorithms (GA), ant colony optimization (ACO), or others. In these hybrid approaches, the ACO has effectively optimized the solution of many benchmark problems in the quadratic assignment problem library. In this paper, we propose a novel hybrid method that combines the effective chaotic search algorithm that has better performance than the tabu search and global search algorithms such as ACO and GA. Our results show that the proposed chaotic hybrid algorithm has better performance than the conventional chaotic search and conventional hybrid algorithms. In addition, we show that chaotic search algorithm combined with ACO has better performance than when combined with GA.
NASA Astrophysics Data System (ADS)
Ayvaz, M. Tamer
2016-07-01
In this study, a new simulation-optimization approach is proposed for solving the areal groundwater pollution source identification problems which is an ill-posed inverse problem. In the simulation part of the proposed approach, groundwater flow and pollution transport processes are simulated by modeling the given aquifer system on MODFLOW and MT3DMS models. The developed simulation model is then integrated to a newly proposed hybrid optimization model where a binary genetic algorithm and a generalized reduced gradient method are mutually used. This is a novel approach and it is employed for the first time in the areal pollution source identification problems. The objective of the proposed hybrid optimization approach is to simultaneously identify the spatial distributions and input concentrations of the unknown areal groundwater pollution sources by using the limited number of pollution concentration time series at the monitoring well locations. The applicability of the proposed simulation-optimization approach is evaluated on a hypothetical aquifer model for different pollution source distributions. Furthermore, model performance is evaluated for measurement error conditions, different genetic algorithm parameter combinations, different numbers and locations of the monitoring wells, and different heterogeneous hydraulic conductivity fields. Identified results indicated that the proposed simulation-optimization approach may be an effective way to solve the areal groundwater pollution source identification problems.
An adaptive metamodel-based global optimization algorithm for black-box type problems
NASA Astrophysics Data System (ADS)
Jie, Haoxiang; Wu, Yizhong; Ding, Jianwan
2015-11-01
In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.
A modified form of conjugate gradient method for unconstrained optimization problems
NASA Astrophysics Data System (ADS)
Ghani, Nur Hamizah Abdul; Rivaie, Mohd.; Mamat, Mustafa
2016-06-01
Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947-951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.
A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem
NASA Technical Reports Server (NTRS)
Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.
2002-01-01
In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.
NASA Astrophysics Data System (ADS)
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
Solution to Electric Power Dispatch Problem Using Fuzzy Particle Swarm Optimization Algorithm
NASA Astrophysics Data System (ADS)
Chaturvedi, D. K.; Kumar, S.
2015-03-01
This paper presents the application of fuzzy particle swarm optimization to constrained economic load dispatch (ELD) problem of thermal units. Several factors such as quadratic cost functions with valve point loading, ramp rate limits and prohibited operating zone are considered in the computation models. The Fuzzy particle swarm optimization (FPSO) provides a new mechanism to avoid premature convergence problem. The performance of proposed algorithm is evaluated on four test systems. Results obtained by proposed method have been compared with those obtained by PSO method and literature results. The experimental results show that proposed FPSO method is capable of obtaining minimum fuel costs in fewer numbers of iterations.
The problem of optimal placement of sub-resolution assist features (SRAF)
NASA Astrophysics Data System (ADS)
Mukherjee, Maharaj; Mansfield, Scott; Liebmann, Lars; Lvov, Alexey; Papadapoulou, Evanthia; Lavin, Mark; Zhao, Zengqin
2005-05-01
In this paper, we present a formulation of the Sub-Resolution Assist Feature (SRAF) placement problem as a geometric optimization problem. We present three independent geometric methodologies that use the above formulation to optimize SRAF placements under mask and lithographic process constraints. Traditional rules-based methodology, are mainly one dimensional in nature. These methods, though apparently very simple, has proven to be inadequate for complex two-dimensional layouts. The methodologies presented in this paper, on the other hand, are inherently two-dimensional and attempt to maximize SRAF coverage on real and complex designs, and minimizes mask rule and lithographic violations.
NASA Astrophysics Data System (ADS)
Campbell, Stephen L.; Marz, Roswitha
2007-05-01
Direct transcription methods are used to solve optimal control problems in many industrial settings. Models for physical systems often take the form of differential algebraic equations (DAEs). The index of the DAE traditionally is viewed as an important factor in deciding whether a particular numerical approach should be used. Recently it has been observed that what the user thinks is the index of the DAE may not be the same as the index available to the optimization software. An investigation of this fact is underway in order to develop guidelines to assist users of various numerical optimal control packages. This paper develops some theoretical results that will be needed for this development.
Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei; Biteus, Jonas
2014-12-10
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.
Coelho, V N; Coelho, I M; Souza, M J F; Oliveira, T A; Cota, L P; Haddad, M N; Mladenovic, N; Silva, R C P; Guimarães, F G
2016-01-01
This article presents an Evolution Strategy (ES)--based algorithm, designed to self-adapt its mutation operators, guiding the search into the solution space using a Self-Adaptive Reduced Variable Neighborhood Search procedure. In view of the specific local search operators for each individual, the proposed population-based approach also fits into the context of the Memetic Algorithms. The proposed variant uses the Greedy Randomized Adaptive Search Procedure with different greedy parameters for generating its initial population, providing an interesting exploration-exploitation balance. To validate the proposal, this framework is applied to solve three different [Formula: see text]-Hard combinatorial optimization problems: an Open-Pit-Mining Operational Planning Problem with dynamic allocation of trucks, an Unrelated Parallel Machine Scheduling Problem with Setup Times, and the calibration of a hybrid fuzzy model for Short-Term Load Forecasting. Computational results point out the convergence of the proposed model and highlight its ability in combining the application of move operations from distinct neighborhood structures along the optimization. The results gathered and reported in this article represent a collective evidence of the performance of the method in challenging combinatorial optimization problems from different application domains. The proposed evolution strategy demonstrates an ability of adapting the strength of the mutation disturbance during the generations of its evolution process. The effectiveness of the proposal motivates the application of this novel evolutionary framework for solving other combinatorial optimization problems.
The role of optimism in the process of schema-focused cognitive therapy of personality problems.
Hoffart, Asle; Sexton, Harold
2002-06-01
The aim of this study was to examine the determinants and effects of optimism in the process of schema-focused cognitive therapy of personality problems. The sample consisted of 35 patients with panic disorder and/or agoraphobia and DSM-IV Cluster C personality traits who participated in an 11-week residential program with one symptom-focused and one personality-focused phase. This study examines the role played by optimism during the individual sessions of the second phase, using a time series approach. Decreased patient's belief in his/her primary Early Maladaptive Schema and increased patient-experienced empathy from the therapist in a session predicted increased patient-rated optimism before the subsequent session. Increased patient-rated optimism in turn predicted decreased schema belief and distress and increased insight, empathy, and therapist-rated optimism. The slope of optimism across sessions was related to change in most of the overall outcome measures. There appears to be a positive feedback in the process of schema-focused cognitive therapy between decreased schema belief and increased optimism. In addition, optimism appears to mediate the effects of schema belief and therapist empathy on overall improvement, and to serve as an antecedent to decreased distress and to increased empathy, insight, and therapist's optimism.
Casas, E.
1999-03-15
In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem.
An Optimization Model for Scheduling Problems with Two-Dimensional Spatial Resource Constraint
NASA Technical Reports Server (NTRS)
Garcia, Christopher; Rabadi, Ghaith
2010-01-01
Traditional scheduling problems involve determining temporal assignments for a set of jobs in order to optimize some objective. Some scheduling problems also require the use of limited resources, which adds another dimension of complexity. In this paper we introduce a spatial resource-constrained scheduling problem that can arise in assembly, warehousing, cross-docking, inventory management, and other areas of logistics and supply chain management. This scheduling problem involves a twodimensional rectangular area as a limited resource. Each job, in addition to having temporal requirements, has a width and a height and utilizes a certain amount of space inside the area. We propose an optimization model for scheduling the jobs while respecting all temporal and spatial constraints.
Approximate dynamic programming recurrence relations for a hybrid optimal control problem
NASA Astrophysics Data System (ADS)
Lu, W.; Ferrari, S.; Fierro, R.; Wettergren, T. A.
2012-06-01
This paper presents a hybrid approximate dynamic programming (ADP) method for a hybrid dynamic system (HDS) optimal control problem, that occurs in many complex unmanned systems which are implemented via a hybrid architecture, regarding robot modes or the complex environment. The HDS considered in this paper is characterized by a well-known three-layer hybrid framework, which includes a discrete event controller layer, a discrete-continuous interface layer, and a continuous state layer. The hybrid optimal control problem (HOCP) is to nd the optimal discrete event decisions and the optimal continuous controls subject to a deterministic minimization of a scalar function regarding the system state and control over time. Due to the uncertainty of environment and complexity of the HOCP, the cost-to-go cannot be evaluated before the HDS explores the entire system state space; as a result, the optimal control, neither continuous nor discrete, is not available ahead of time. Therefore, ADP is adopted to learn the optimal control while the HDS is exploring the environment, because of the online advantage of ADP method. Furthermore, ADP can break the curses of dimensionality which other optimizing methods, such as dynamic programming (DP) and Markov decision process (MDP), are facing due to the high dimensions of HOCP.
Numerical study of the inverse problem for the diffusion-reaction equation using optimization method
NASA Astrophysics Data System (ADS)
Soboleva, O. V.; Brizitskii, R. V.
2016-04-01
The model of transfer of substance with mixed boundary condition is considered. The inverse extremum problem of identification of the main coefficient in a nonstationary diffusion-reaction equation is formulated. The numerical algorithm based on the Newton-method of nonlinear optimization and finite difference discretization for solving this extremum problem is developed and realized on computer. The results of numerical experiments are discussed.
A methodology to find the elementary landscape decomposition of combinatorial optimization problems.
Chicano, Francisco; Whitley, L Darrell; Alba, Enrique
2011-01-01
A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.
An investigation of exploitation versus exploration in GBEA optimization of PORS 15 and 16 Problems
Koch, Kaelynn
2012-01-01
It was hypothesized that the variations in time to solution are driven by the competing mechanisms of exploration and exploitation.This thesis explores this hypothesis by examining two contrasting problems that embody the hypothesized tradeoff between exploration and exploitation. Plus one recall store (PORS) is an optimization problem based on the idea of a simple calculator with four buttons: plus, one, store, and recall. Integer addition and store are classified as operations, and one and memory recall are classified as terminals. The goal is to arrange a fixed number of keystrokes in a way that maximizes the numerical result. PORS 15 (15 keystrokes) represents the subset of difficult PORS problems and PORS 16 (16 keystrokes) represents the subset of PORS problems that are easiest to optimize. The goal of this work is to examine the tradeoff between exploitation and exploration in graph based evolutionary algorithm (GBEA) optimization. To do this, computational experiments are used to examine how solutions evolve in PORS 15 and 16 problems when solved using GBEAs. The experiment is comprised of three components; the graphs and the population, the evolutionary algorithm rule set, and the example problems. The complete, hypercube, and cycle graphs were used for this experiment. A fixed population size was used.
Bacanin, Nebojsa; Tuba, Milan
2014-01-01
Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.
Grid optimization and multigrid techniques for fluid flow and transport problems
NASA Astrophysics Data System (ADS)
Pardhanani, Anand L.
1992-01-01
Special numerical techniques for the efficient and accurate solution of fluid flow and certain other transport processes are investigated. These include adaptive redistribution and optimization of computational grids, multigrid techniques for convection-diffusion problems, and multigrid time-marching methods for non-stationary and nonlinear problems. The grid optimization strategy is based on constructing and minimizing a mathematical objective function which defines the desired grid properties. For convection-diffusion problems, it is demonstrated that standard multigrid techniques fail when the coarse grids violate mesh-size restrictions. A variety of alternate multigrid strategies are explored, including artificial dissipation, fine grid pre-elimination, self-adjoint formulation, defect correction, and combination with grid redistribution. Multilevel techniques are also developed for time-dependent problems, including evolution problems with non-steady or transient solutions, and steady-state problems solved with artificial time-marching. Both explicit and implicit integration schemes are investigated, and it is shown that significant performance improvements can be gained with the use of multigrid. These techniques are implemented and tested on representative model problems as well as practical applications of current research interest. The grid investigations involve optimization in model problems, and in large-scale 3-D aircraft wing-body configurations. The multigrid applications range from model convection-diffusion problems, to time-dependent problems, to coupled nonlinear problems in two major application areas. The first application involves simulating spatio-temporal patterns in a coupled, nonlinear, reaction-diffusion problem that models the behavior of the Belousov-Zhabotinskii reaction. This multi-species reaction, which exhibits intricate patterns in laboratory experiments, has attracted considerable interest in the field of nonlinear dynamics. The
Nash, Stephen G.
2013-11-11
The research focuses on the modeling and optimization of nanoporous materials. In systems with hierarchical structure that we consider, the physics changes as the scale of the problem is reduced and it can be important to account for physics at the fine level to obtain accurate approximations at coarser levels. For example, nanoporous materials hold promise for energy production and storage. A significant issue is the fabrication of channels within these materials to allow rapid diffusion through the material. One goal of our research is to apply optimization methods to the design of nanoporous materials. Such problems are large and challenging, with hierarchical structure that we believe can be exploited, and with a large range of important scales, down to atomistic. This requires research on large-scale optimization for systems that exhibit different physics at different scales, and the development of algorithms applicable to designing nanoporous materials for many important applications in energy production, storage, distribution, and use. Our research has two major research thrusts. The first is hierarchical modeling. We plan to develop and study hierarchical optimization models for nanoporous materials. The models have hierarchical structure, and attempt to balance the conflicting aims of model fidelity and computational tractability. In addition, we analyze the general hierarchical model, as well as the specific application models, to determine their properties, particularly those properties that are relevant to the hierarchical optimization algorithms. The second thrust was to develop, analyze, and implement a class of hierarchical optimization algorithms, and apply them to the hierarchical models we have developed. We adapted and extended the optimization-based multigrid algorithms of Lewis and Nash to the optimization models exemplified by the hierarchical optimization model. This class of multigrid algorithms has been shown to be a powerful tool for
Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah
2016-01-01
The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.
NASA Astrophysics Data System (ADS)
Goldberg, Daniel N.; Krishna Narayanan, Sri Hari; Hascoet, Laurent; Utke, Jean
2016-05-01
We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.
Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah
2016-01-01
The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585
An optimal control problem for a time-dependent Ginzburg-Landau model of superconductivity
NASA Astrophysics Data System (ADS)
Lin, Haomin
The motion of vortices in a Type II superconductor destroys the material's superconductivity because it dissipates energy and causes resistance. When a transport current is applied to a clean Type-II superconductor in the mixed state, the vortices will go into motion due to the induced Lorentz force and thus the superconductivity of the material is lost. However, various pinning mechanisms, such as normal inclusions, can inhibit vortex motion and pin the vortices to specific sites. We demonstrate that the placement of the normal inclusion sites has an important effect on the largest electrical current that can be applied to the superconducting material while all vortices remain stationary. Here, an optimal control problem using a time dependent Ginzburg-Landau model is proposed to seek numerically the optimal locations of the normal inclusion sites. An analysis of this optimal control problem is performed, the existence of an optimal control solution is proved and a sensitivity system is given. We then derive a gradient method to solve this optimal control problem. Numerical simulations are performed and the results are presented and discussed.
A new pragmatic approach to solve the problems of vector optimization with uncertain parameters
NASA Astrophysics Data System (ADS)
Reizlin, V. I.; Nefedova, A. A.
2016-04-01
In this paper, we consider the method for solving problems of multi-criteria optimization with mathematical models that contain a lot of variables. The values of these variables are not regulated by a decision-maker. We introduce a new concept of 'tolerance of the decision variant'. This concept is similar to such concepts as stability, survivability, etc.
NASA Astrophysics Data System (ADS)
Guo, Peng; Cheng, Wenming; Wang, Yi
2014-10-01
The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.
Constrained Optimization Problems in Cost and Managerial Accounting--Spreadsheet Tools
ERIC Educational Resources Information Center
Amlie, Thomas T.
2009-01-01
A common problem addressed in Managerial and Cost Accounting classes is that of selecting an optimal production mix given scarce resources. That is, if a firm produces a number of different products, and is faced with scarce resources (e.g., limitations on labor, materials, or machine time), what combination of products yields the greatest profit…
On Numerical Methods of Solving Some Optimal Path Problems on the Plane
NASA Astrophysics Data System (ADS)
Ushakov, V. N.; Matviychuk, A. R.; Malev, A. G.
Three numerical methods of solution of some time optimal control problems for a system under phase constraints are described in the paper. Two suggested methods are based on transition to the discrete time model, constructing attainability sets and application of the guide construction. The third method is based on the Deikstra algorithm.
Masiero, Federica
2007-05-15
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
The Soda Can Optimization Problem: Getting Close to the Real Thing
ERIC Educational Resources Information Center
Premadasa, Kirthi; Martin, Paul; Sprecher, Bryce; Yang, Lai; Dodge, Noah-Helen
2016-01-01
Optimizing the dimensions of a soda can is a classic problem that is frequently posed to freshman calculus students. However, if we only minimize the surface area subject to a fixed volume, the result is a can with a square edge-on profile, and this differs significantly from actual cans. By considering a more realistic model for the can that…