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Solving convex problems involving powers using conic optimization  

E-print Network

Solving convex problems involving powers using conic optimization and a new self-concordant barrier CFG 07 Heidelberg University CFG 07 Solving convex problems involving powers using conic optimization 1 #12;Overview 1. Motivation Why convex optimization? Why a conic formulation? 2. Unified conic

Glineur, François


Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

Formulating Cyber-Security as Convex Optimization ProblemsĂ? Kyriakos G. Vamvoudakis1 , Jo~ao P,vigna} Abstract. Mission-centric cyber-security analysts require a complete overview and understanding The Flag (iCTF) hacking competition. Keywords: Cyber-Security, Convex Optimization, System Identifica- tion

Vigna, Giovanni


Formulating Cyber-Security as Convex Optimization Problems  

E-print Network

Formulating Cyber-Security as Convex Optimization Problems Kyriakos G. Vamvoudakis, Jo~ao P. Mission-centric cyber-security analysts require a complete overview and understanding of the state. Keywords: Cyber-Security, Convex Optimization, System Identifica- tion, iCTF 1 Introduction Guaranteeing

Hespanha, JoĂŁo Pedro


Convex Formulations of Aggregate Network Air Traffic Flow Optimization Problems  

E-print Network

Control Center. I. INTRODUCTION Research on the steady increase in air traffic volume has triggeredConvex Formulations of Aggregate Network Air Traffic Flow Optimization Problems Daniel B. Work, Student Member, IEEE, Alexandre M. Bayen, Member, IEEE Abstract--The problem of regulating air traffic


A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems  

PubMed Central

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z.; Ye, Jieping



Global optimization of a nonconvex single facility location problem by sequential unconstrained convex minimization  

Microsoft Academic Search

The problem of maximizing the sum of certain composite functions, where each term is the composition of a convex decreasing function, bounded from below, with a convex function having compact level sets arises in certain single facility location problems with gauge distance functions. We show that this problem is equivalent to a convex maximization problem over a compact convex set

Hoang Tuy; Faiz A. Al-Khayyal



An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization  

E-print Network

An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization topology, the delay can be controlled by varying the sizes of transistors in the circuit. Here, the size of a transistor is measured in terms of its channel width, since the channel lengths in a digital circuit

Sapatnekar, Sachin


Optimal sets for a class of minimization problems with convex constraints  

E-print Network

We look for the minimizers of the functional $\\jla{\\la}(\\oo)=\\la|\\oo|-P(\\oo)$ among planar convex domains constrained to lie into a given ring. We prove that, according to the values of the parameter $\\la$, the solutions are either a disc or a polygon. In this last case, we describe completely the polygonal solutions by reducing the problem to a finite dimensional optimization problem. We recover classical inequalities for convex sets involving area, perimeter and inradius or circumradius and find a new one.

Bianchini, Chiara



Conic optimization: an elegant framework for convex optimization  

E-print Network

Conic optimization: an elegant framework for convex optimization Fran¸cois Glineur Service de Math the reader to a very elegant formu- lation of convex optimization problems called conic optimization is in- troduced, which leads to the conic formulation of convex optimization problems. This formulation

Glineur, François


Generalized convex functions: properties, optimality and duality  

SciTech Connect

It is shown that a set which is closed and locally star shaped at each of its points is convex. Moreover, a semilocally convex function on a closed set which is also lower semi-continuous is a convex function. A characterization is given for a function to be semilocally convex. For a nonlinear programming problem involving semilocally convex functions, a dual is associated and necessary optimality conditions derived.

Kaul, R.N.; Kaur, S.



Implicit optimality criterion for convex SIP problem with box constrained index set  

Microsoft Academic Search

We consider a convex problem of Semi-Infinite Programming (SIP) with a multidimensional index set defined by a finite number\\u000a of box constraints. In study of this problem we apply the approach suggested in Kostyukova et al. (Int. J. Math. Stat. 13(J08):13–33,\\u000a 2008) for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their

O. I. Kostyukova; T. V. Tchemisova



The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications  

PubMed Central

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J. Jim; Zhang, Ping



The optimal solution of a non-convex state-dependent LQR problem and its applications.  


This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417

Xu, Xudan; Zhu, J Jim; Zhang, Ping




E-print Network

- formation of some kind it is often impossible to incorporate this in the Kalman filter framework. We will give a very brief introduction to con- vex optimization (see also [2]). The main message in convex of a stochastic variable z that maximizes the conditional density p(z|y), given the observation y (y Rny and z

Schön, Thomas


On the Complexity of Optimization Problems for 3Dimensional Convex Polyhedra and Decision Trees \\Lambda  

E-print Network

]). They are the product of convex hull algorithms, and are key components for problems in robot motion planning and computer­aided geometric design. Moreover, due to a beautiful theorem of Steinitz [20, 38], they provide at the design of small linear decision trees to represent a multi­category point set (e.g., see [5, 6, 8, 21, 29

Goodrich, Michael T.


Advances in Convex Optimization: Conic Programming  

E-print Network

Advances in Convex Optimization: Conic Programming Arkadi Nemirovski Abstract. During the last two decades, major developments in Convex Optimization were focusing on Conic Programming, primarily, on Linear, Conic Quadratic and Semidef- inite optimization. Conic Programming allows to reveal rich

Nemirovski, Arkadi


A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem  

Microsoft Academic Search

Economic dispatch (ED) plays an important role in power system operation. ED problem is a non-smooth and non-convex problem when valve-point effects of generation units are taken into account. This paper presents an efficient hybrid evolutionary approach for solving the ED problem considering the valve-point effect. The proposed algorithm combines a fuzzy adaptive particle swarm optimization (FAPSO) algorithm with Nelder–Mead

Taher Niknam




E-print Network

­ formation of some kind it is often impossible to incorporate this in the Kalman filter framework. We will give a very brief introduction to con­ vex optimization (see also [2]). The main message in convex of a stochastic variable z that maximizes the conditional density p(zjy), given the observation y (y 2 R ny and z

Gustafsson, Fredrik


Parallel MRI Reconstruction by Convex Optimization  

E-print Network

In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem. A class of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA. It is shown in this paper that, if only the magnitude image is reconstructed, there exists a convex solution space for the magnitude image and sensitivity encoded images. This solution space enables formulation of a regularized convex optimization problem and leads to a globally optimal and unique solution for the magnitude image reconstruction. Its applications to in-vivo MRI data sets result in superior reconstruction performance compared with other algorithms.

Zhang, Cishen



A conic approach for separable convex optimization  

E-print Network

' & $ % A conic approach for separable convex optimization Fran#24;cois Glineur Aspirant F programmation math#19;ematique Han-sur-Lesse, February 2, 2001 #12; A conic approach for separable convex optimization ' & $ % #11; #8; Outline Introduction #5; Conic optimization #5; Geometric optimization

Glineur, François


Convex initialization of the H2-optimal static output feedback problem Henrik Manum, Sigurd Skogestad, and Johannes Jaschke  

E-print Network

can be found by solving an iterative Riccati equation. For the case with white noise assumption on x0 is unsolved [4] so one cannot expect to find an analytic or convex numerical solution. The contribution

Skogestad, Sigurd


Stochastic Convex Optimization Shai Shalev-Shwartz  

E-print Network

-trivial learnability. 1 Introduction We consider the stochastic convex minimization problem argmin wW F(w) (1) where F(w) = EZ [f(w; Z)] is the expectation, with re- spect to Z, of a random objective that is convex in w is to choose w based on the sample and full knowledge of f(·, ·) and W so as to minimize F(w). Alternatively


Numerical approximation of young measuresin non-convex variational problems  

Microsoft Academic Search

  \\u000a \\u000a \\u000a Summary. In non-convex optimisation problems, in particular in non-convex variational problems, there usually does not exist any classical\\u000a solution but only generalised solutions which involve Young measures. In this paper, first a suitable relaxation and approximation\\u000a theory is developed together with optimality conditions, and then an adaptive scheme is proposed for the efficient numerical\\u000a treatment. The Young measures solving

Carsten Carstensen; Tomáš Roubí?ek



Complexity of convex optimization using geometry-based measures and a reference point  

E-print Network

Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \\in P, where P is a closed convex set. We bound the complexity of computing an almost-optimal solution of this problem ...

Freund, Robert M.



A block coordinate gradient descent method for regularized convex separable optimization and covariance selection  

Microsoft Academic Search

We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of\\u000a a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem\\u000a includes the covariance selection problem that can be expressed as an ?\\u000a 1-penalized maximum likelihood estimation problem. In this

Sangwoon Yun; Paul Tseng; Kim-Chuan Toh


Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization  

Microsoft Academic Search

The strong conical hull intersection property and bounded linear regularity are propertiesof a collection of finitely many closed convex intersecting sets in Euclidean space.These fundamental notions occur in various branches of convex optimization (constrainedapproximation, convex feasibility problems, linear inequalities, for instance).It is shown that the standard constraint qualification from convex analysis impliesbounded linear regularity, which in turn yields the strong

Heinz H. Bauschke; Jonathan M. Borwein; Wu Li



Optimality conditions for nondifferentiable convex semi-infinite programming  

Microsoft Academic Search

This paper gives characterizations of optimal solutions to the nondifferentiable convex semi-infinite programming problem,\\u000a which involve the notion of Lagrangian saddlepoint. With the aim of giving the necessary conditions for optimality, local\\u000a and global constraint qualifications are established. These constraint qualifications are based on the property of Farkas-Minkowski,\\u000a which plays an important role in relation to certain systems obtained by

M. A. López; E. Vercher



A unified conic formulation for convex problems involving powers  

E-print Network

A unified conic formulation for convex problems involving powers Fran¸cois Glineur francois / MOPTA 07 A unified conic formulation for convex problems involving powers 1 #12;Overview 1. Motivation ICCOPT II / MOPTA 07 A unified conic formulation for convex problems involving powers 2 #12;Overview 1

Glineur, François


Greedy approximation in convex optimization  

E-print Network

Jun 2, 2012 ... continuous functions. One more important argument that motivates us to ... In optimization theory an energy function E(x) is given and we should find an approximate ..... of matrices with nuclear norm not exceeding 1. We are ...



Optimal partitions having disjoint convex and conic hulls  

Microsoft Academic Search

LetA1,?,An be distinctk-dimensional vectors. We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set. We show that there exists an optimal partition whose sets have (pairwise) disjoint conic hulls. We also show that if the number of vectors in each of

E. R. Barnes; Alan J. Hoffman; Uriel G. Rothblum



Universal Duality in Conic Convex Optimization Simon P. Schurr  

E-print Network

Universal Duality in Conic Convex Optimization Simon P. Schurr Andr´e L. Tits Dianne P. O is feasible. For a pair of dual conic convex programs, we provide simple conditions on the "constraint) they are metrically and topologically generic; and (iii) they can be verified by solving a single conic convex program

O'Leary, Dianne P.


Universal Duality in Conic Convex Optimization Simon P. Schurr  

E-print Network

Universal Duality in Conic Convex Optimization Simon P. Schurr Andr´e L. Tits Dianne P. O either the primal or dual is feasible. For a pair of dual conic convex programs, we provide simple be verified by solving a single conic convex program. We relate to universal duality the fact

Tits, André


Neural network for solving convex quadratic bilevel programming problems.  


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. PMID:24333480

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie



Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization  

Microsoft Academic Search

.   The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many\\u000a closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization\\u000a (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard\\u000a constraint qualification from convex analysis implies bounded linear regularity,

Heinz H. Bauschke; Jonathan M. Borwein; Wu Li



Optimization Online - Convex Relaxations of Non-Convex Mixed ...  

E-print Network

Nov 14, 2008 ... ... of Non-Convex Mixed Integer Quadratically Constrained Programs: Projected ... We also propose a new "eigen reformulation" for MIQCP, and a cut ... take up to a couple of hours to solve using a state-of-the-art SDP solver.

Anureet Saxena



Distributionally Robust Convex Optimization - Optimization Online  

E-print Network

1Imperial College Business School, Imperial College London, United Kingdom ... lenging problems ranging from engineering design, finance and machine learning to ... properties of Q0 from existing domain knowledge (e.g., bounds on the ...



On the Fermat-Lagrange principle for mixed smooth convex extremal problems  

SciTech Connect

A simple geometric condition that can be attached to an extremal problem of a fairly general form included in a family of problems is indicated. This is used to demonstrate that the task of formulating a uniform condition for smooth convex problems can be satisfactorily accomplished. On the other hand, the necessity of this new condition of optimality is proved under certain technical assumptions.

Brinkhuis, Ya [Erasmus University Rotterdam, Econometric Institute, Rotterdam (Netherlands)



Newton-Raphson consensus for distributed convex optimization  

E-print Network

Newton-Raphson consensus for distributed convex optimization Luca Schenato joint work with A of Padova April 28th, 2011 (DEI - UniPD) Distrib. Newton-Raphson optimization April 28PD) Distrib. Newton-Raphson optimization April 28th, 2011 2 / 26 #12;Introduction Distribution optimization

Schenato, Luca


6.253 Convex Analysis and Optimization, Spring 2010  

E-print Network

This course will focus on fundamental subjects in (deterministic) optimization, connected through the themes of convexity, geometric multipliers, and duality. The aim is to develop the core analytical and computational ...

Bertsekas, Dimitri


A simplicial branch and duality bound algorithm for the sum of convex-convex ratios problem  

NASA Astrophysics Data System (ADS)

This article presents a simplicial branch and duality bound algorithm for globally solving the sum of convex-convex ratios problem with nonconvex feasible region. To our knowledge, little progress has been made for globally solving this problem so far. The algorithm uses a branch and bound scheme where the Lagrange duality theory is used to obtain the lower bounds. As a result, the lower-bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently. It has been proved that the algorithm possesses global convergence. Finally, the numerical experiments are given to show the feasibility of the proposed algorithm.

Shen, Pei-Ping; Duan, Yun-Peng; Pei, Yong-Gang



Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.  


In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning. PMID:17148822

Hoffmann, Aswin L; Siem, Alex Y D; den Hertog, Dick; Kaanders, Johannes H A M; Huizenga, Henk



Convex Optimization Theory Athena Scientific, 2009  

E-print Network

for Conic Programming . . p. 346 6.8. Approximate Subgradient Methods . . . . . . . . . p. 347 6 is typically a conjugate function (cf. Section 4.2.1), which is generically closed and convex, but often non together with its special case, conic duality. Both of these duality structures arise often in applications

Recht, Ben


10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method  

E-print Network

10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method Lecturer: Barnabas Poczos.1 Motivation Newton method is originally developed for finding a root of a function. It is also known as Newton- Raphson method. The problem can be formulated as, given a function f : R R, finding the point x

Tibshirani, Ryan



E-print Network

ON THE RELATION BETWEEN OPTION AND STOCK PRICES: A CONVEX OPTIMIZATION APPROACH DIMITRIS BERTSIMAS of option and stock prices based just on the no-arbitrage assumption, but without assuming any model on this relation. For the single stock problem, given moments of the prices of the underlying assets, we show

Bertsimas, Dimitris


Online Convex Programming and Generalized Infinitesimal GradientAscent  

Microsoft Academic Search

Convex programming involves a convex set F Rn and a convex cost function c : F ! R. The goal of convex programming is to nd a point in F which minimizes c. In online convex programming, the convex set is known in advance, but in each step of some repeated optimization problem, one must select a point inF before

Martin Zinkevich



Operation and Configuration of a Storage Portfolio via Convex Optimization  

E-print Network

is equally broad, and includes pumped hydro, compressed air energy storage (CAES), battery energy storage sysOperation and Configuration of a Storage Portfolio via Convex Optimization Matt Kraning, Yang Wang consider a portfolio of storage devices which is used to modify a commodity flow so as to minimize


Operation and Configuration of a Storage Portfolio via Convex Optimization  

E-print Network

is equally broad, and includes pumped hydro, compressed air energy storage (CAES), battery energy storage sysOperation and Configuration of a Storage Portfolio via Convex Optimization Matt Kraning, Yang Wang University; email: {mkraning, yw224, ekine, boyd} Abstract: We consider a portfolio of storage


Newton-Raphson consensus for distributed convex optimization  

E-print Network

Newton-Raphson consensus for distributed convex optimization Luca Schenato Department;Presentation outline Motivations State-of-the-art Centralized Newton-Raphson: a quick overview Consensus-based Newton-Raphson Convergence properties (theory + simulations) Future directions 6 #12;Presentation outline

Schenato, Luca


Efficient Convex Optimization Approaches to Variational Image Fusion  

E-print Network

Efficient Convex Optimization Approaches to Variational Image Fusion Jing Yuan1 , Brandon Miles1 of Bergen Bergen, Norway Abstract. Image fusion is an imaging technique to visualize informa imaging etc. In this work, we study two variational approaches to image fusion which are closely related

Soatto, Stefano


Convexity-Based Optimization for Power-Delay Tradeoff using Transistor Sizing Mahesh Ketkar, and Sachin S. Sapatnekar  

E-print Network

Convexity-Based Optimization for Power-Delay Tradeoff using Transistor Sizing Mahesh Ketkar. In [3], the power optimization problem is solved by transistor sizing and ordering. Power dissipation of transistor sizing is not considered. Recently an accurate technique for circuit optimization has been

Sapatnekar, Sachin


sensitivity analysis in convex quadratic optimization: simultaneous ...  

E-print Network

of using optimal bases in parametric LO showing by an example that different ...... maximization game correspond to optimal solutions of the following quadratic minimization .... mization, Springer Science+Business Media, New York, USA.



Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems  

Microsoft Academic Search

In Akrotirianakis and Floudas (2004) we presented the theoretical foundations of a new class of convex underestimators for C2 nonconvex functions. In this paper, we present computational experience with those underestimators incorporated within a Branch-and-Bound algorithm for box-conatrained problems. The algorithm can be used to solve global optimization problems that involve C2 functions. We discuss several ways of incorporating the

Ioannis G. Akrotirianakis; Christodoulos A. Floudas



The Existence Problem for Steiner Networks in Strictly Convex Domains  

NASA Astrophysics Data System (ADS)

We consider the existence problem for `Steiner networks' (trivalent graphs with 2 ?/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.

Freire, Alexandre



The Convex Geometry of Linear Inverse Problems  

E-print Network

Dec 2, 2010 ... In order to address this problem we give a hierarchy of semidefinite .... fruitful applications in problems in approximation theory of various function ... polytope, the permutahedron also needs to be recentered about the point 1.



Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach  

E-print Network

. Keywords: utility maximization, small transaction costs, duality, shadow price MSC Subject Classification of consistent price systems or shadow price processes, which allow to translate the original problem into a more costs. In the present paper, we carry out a convex duality approach facilitated by the concept of shadow

Kallsen, Jan


FIR Filter Design via Spectral Factorization and Convex Optimization 1 FIR Filter Design via Spectral Factorization  

E-print Network

is optimization variable fi are convex: for 0 1, fix + 1 ,y fix + 1 ,fiy examples: linear & convex quadratic 1000s variables, 10000s constraints feasible on PC FIR Filter Design via Spectral FactorizationFIR Filter Design via Spectral Factorization and Convex Optimization 1 FIR Filter Design via


On an Extension of Condition Number Theory to Non-Conic Convex Optimization  

E-print Network

On an Extension of Condition Number Theory to Non-Conic Convex Optimization Robert M. Freund, the modern theory of condition numbers for conic convex optimization: z := minx ctx s.t. Ax - b CY x CX , to the more general non-conic format: (GPd) z := minx ctx s.t. Ax - b CY x P , where P is any closed convex

Ordóñez, Fernando


Optimal Monetary Policy with a Convex Phillips Curve  

E-print Network

assumption that nominal wages are flexible upwards but rigid downwards, so that inflation is a decreasing and convex function of the unemployment rate–equivalently, an increasing function of the output gap; see Layard et al. (1991) and Nickell (1997... bias even when policymakers target the natural unemployment rate, that is when they operate with pru- dent discretion, and their loss function is symmetric. Optimal mon- etary policy also induces positive co-movement between average in- flation, average...

Tambakis, Demosthenes N



E-print Network

problems, involving undiscounted utility function and differential inclusions ... study of stability of ordinary differential equations with un-known terminal values for ... This means that in this case the inequality (4) is satisfied for all x, y with c(x) < 0 ...



Convex Optimization of Centralized Inventory Operations  

E-print Network

Jan 10, 2005 ... There are many real-life examples where companies attempt to reduce inventory and ... Sciences, University of Iowa, Iowa City, IA 52242-1000, USA. ...... The effect is a tightening, in the sense that the optimal value of the new ...



Tensor Principal Component Analysis via Convex Optimization  

E-print Network

Dec 9, 2012 ... tensor, known as the tensor principal component analysis (PCA) problem. ...... experiments in this paper were conducted on an Intel Core i5-2520M ...... In Medical Image Computing and Computer-Assisted Intervention,.



Maximum principle for state and mixed constrained problems with equality and inequality mixed constraints: Convex case  

NASA Astrophysics Data System (ADS)

Here we derive necessary conditions of optimality for optimal control problems with both state and mixed constraints in the form of nonsmooth maximum principle. A special feature of our main result is that the mixed constraints may appear in both the equality and inequality form. These conditions are stated in terms of a "joint" subdifferential with respect to both state and control variables. The use of the "joint" subdifferential gives sufficiency for normal, linear convex problems as it can be interfered by an adaptation of [7].

Biswas, M. H. A.; de Pinho, MdR



Convexity and the separability problem of quantum mechanical density matrices  

Microsoft Academic Search

A finite-dimensional quantum mechanical system is modelled by a density?, a trace one, positive semi-definite matrix on a suitable tensor product space H[N]. For the system to demonstrate experimentally certain non-classical behavior, ? cannot be in S, a closed convex set of densities whose extreme points have a specificed tensor product form. Two mathematical problems in the quantum computing literature

Arthur O. Pittenger; Morton H. Rubin



Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics  

NASA Astrophysics Data System (ADS)

This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary approximation techniques like first-order methods and randomization for scalability, and survey the important role of parallel and distributed computation. The new Big Data algorithms are based on surprisingly simple principles and attain staggering accelerations even on classical problems.

Cevher, Volkan; Becker, Stephen; Schmidt, Mark



Target position localization in a passive radar system through convex optimization  

NASA Astrophysics Data System (ADS)

This paper proposes efficient target localization methods for a passive radar system using bistatic time-of-arrival (TOA) information measured at multiple synthetic array locations, where the position of these synthetic array locations is subject to random errors. Since maximum likelihood (ML) formulation of this target localization problem is a non-convex optimization problem, semi-definite relaxation (SDR)-based optimization methods in general do not provide satisfactory performance. As a result, approximated ML optimization problems are proposed and solved with SDR plus bisection methods. For the case without position errors, it is shown that the relaxation guarantees a rank-one solution. The optimization problem for the case with position errors involves only a relaxation of a scalar quadratic term. Simulation results show that the proposed algorithms outperform existing methods and provide mean square position error performance very close to the Cramer-Rao lower bound even for larger values of noise and position estimation errors.

Chalise, Batu K.; Zhang, Yimin D.; Amin, Moeness G.; Himed, Braham



Joint Equalization and Decoding via Convex Optimization  

E-print Network

that users gave to movies, predict the rating (red or dark grey) the given user would give to the given movie. : : : 5 2 State diagrams for noiseless dicode channel without (left) and with precoding (right). The edges are labeled by the input/output pair... for the matrix completion problem. The graph is sparse when there are few ratings. Edges represent ran- dom variables and nodes represent local probabilities. The node probability associated with the ratings implies that each rating depends only on the movie...

Kim, Byung Hak



Globally strongly convex cost functional for a coefficient inverse problem  

E-print Network

A Carleman Weight Function (CWF) is used to construct a new cost functional for a Coefficient Inverse Problems for a hyperbolic PDE. Given a bounded set of an arbitrary size in a certain Sobolev space, one can choose the parameter of the CWF in such a way that the constructed cost functional will be strongly convex on that set. Next, convergence of the gradient method, which starts from an arbitrary point of that set, is established. Since restrictions on the size of that set are not imposed, then this is the global convergence.

Larisa Beilina; Michael V. Klibanov



From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.  


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

Gálvez, Akemi; Iglesias, Andrés



Biogeography-Based Optimization for Different Economic Load Dispatch Problems  

Microsoft Academic Search

This paper presents a biogeography-based optimization (BBO) algorithm to solve both convex and non-convex economic load dispatch (ELD) problems of thermal plants. The proposed methodology can take care of economic dispatch problems involving constraints such as transmission losses, ramp rate limits, valve point loading, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution of biological species. Mathematical

Aniruddha Bhattacharya; Pranab Kumar Chattopadhyay



Optimal Ordered Problem Solver  

Microsoft Academic Search

We introduce a general and in a certain sense time-optimal way of solving one problem after another, efficiently searching the space of programs that compute solution candidates, including those programs that organize and manage and adapt and reuse earlier acquired knowledge. The Optimal Ordered Problem Solver (OOPS) draws inspiration from Levin's Universal Search designed for single problems and universal Turing

Juergen Schmidhuber



Improving beampatterns of two-dimensional random arrays using convex optimization.  


Sensors are becoming ubiquitous and can be combined in arrays for source localization purposes. If classical conventional beamforming is used, then random arrays have poor beampatterns. By pre-computing sensor weights, these beampatterns can be improved significantly. The problem is formulated in the frequency domain as a desired look direction, a frequency-independent transition region, and the power minimized in a rejection-region. Using this formulation, the frequency-dependent sensor weights can be obtained using convex optimization. Since the weights are data independent they can be pre-computed, the beamforming has similar computational complexity as conventional beamforming. The approach is demonstrated for real 2D arrays. PMID:21476620

Gerstoft, Peter; Hodgkiss, William S




NSDL National Science Digital Library

This demo provides a gallery of visual aids that illustrate fundamental concepts for understanding and developing equations that model optimization problems, commonly referred to as max-min problems. Animations, MATLAB routines and Java applets are included.

Roberts, Lila F.; Hill, David R.



Practical iterative image reconstruction in digital breast tomosynthesis by non-convex TpV optimization  

E-print Network

Practical iterative image reconstruction in digital breast tomosynthesis by non-convex Tp tomosynthesis (DBT) is a rapidly developing imaging modality that gives some tomographic information for breast reconstruction, non-convex optimization, tomosynthesis 1. INTRODUCTION Digital breast tomosynthesis (DBT)1

Kurien, Susan



E-print Network

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS Yenming M pattern design, sensor location selection, very large scale arrays, convex op- timization, simulated annealing 1. INTRODUCTION Consider a large scale sensor array having N sensors that monitors a surveillance

Balan, Radu V.


Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization  

NASA Astrophysics Data System (ADS)

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 d^2 different input preparations followed by state tomography via the estimation of the expectation values of d^2-1 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.

Baldwin, Charles; Riofrio, Carlos; Deutsch, Ivan




E-print Network ABSTRACT This work aims at proposing a new reconstruction procedure for structured illumination microscopy reconstruction techniques. Index Terms-- Structured illumination microscopy, image restoration, deconvolutionNON-SMOOTH CONVEX OPTIMIZATION FOR AN EFFICIENT RECONSTRUCTION IN STRUCTURED ILLUMINATION

Condat, Laurent


Bifurcations of indifference points in discrete time optimal control problems  

Microsoft Academic Search

This thesis develops new methods to analyse non-convex discrete time optimal control problems. A distinctive feature of such problems is that indifference states may occur: these are initial states at which several optimising trajectories originate. In the thesis, the genesis of such points through indifference-attractor bifurcations is studied as system parameters are varied. This necessitates an analysis of heteroclinic bifurcation

S. M. Moghayer



Adaptively Constrained Convex Optimization for Accurate Fiber Orientation Estimation with High Order Spherical Harmonics  

PubMed Central

Diffusion imaging data from the Human Connectome Project (HCP) provides a great opportunity to map the whole brain white matter connectivity to unprecedented resolution in vivo. In this paper we develop a novel method for accurately reconstruct fiber orientation distribution from cutting-edge diffusion data by solving the spherical deconvolution problem as a constrained convex optimization problem. With a set of adaptively selected constraints, our method allows the use of high order spherical harmonics to reliably resolve crossing fibers with small separation angles. In our experiments, we demonstrate on simulated data that our algorithm outperforms a popular spherical deconvolution method in resolving fiber crossings. We also successfully applied our method to the multi-shell and diffusion spectrum imaging (DSI) data from HCP to demonstrate its ability in using state-of-the-art diffusion data to study complicated fiber structures. PMID:24505797

Tran, Giang; Shi, Yonggang



Worst-Case Violation of Sampled Convex Programs for Optimization ...  

E-print Network

convex programs and consider the relation between the probability of violation and worst-case violation. ... Key words. Uncertainty, Sampled ... Estimation of the number of random samples N is important to guarantee that the resulting solution



Level Bundle Methods for Constrained Convex Optimization with ...  

E-print Network

May 23, 2013 ... Many optimization problems arising from real-life applications cast into the ... Level bundle methods have at disposal lower bounds (self-built) ... (CV@R?) with confidence level ?; see [27], [28], [7]. ..... (b) Let Kl be the index set belonging to the l-th cycle, it then follows that both ..... Therefore, by developing.



Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithms.  


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 ?0-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. PMID:25064040

Le Thi, Hoai An; Vo, Xuan Thanh; Pham Dinh, Tao



Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions  

E-print Network

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation [bar through "X" symbol] of the sum ...

Agarwal, Alekh


Combining QCR and CHR for Convex Quadratic MINLP Problems ...  

E-print Network

extended QCR method available in the GAMS model library, following a joint project between GAMS, M.C. Plateau, and a research group at the University of ..... Part II: Application to Nonlinear Facility Location,” Working Paper, latest ... Nonlinear Integer Programs with Convex Objective and Linear Constraints,” European.




Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach.  


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. PMID:25232050

Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir



The role of convexity for solving some shortest path problems in plane without triangulation  

NASA Astrophysics Data System (ADS)

Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise a simple O(n) time algorithm for computing the shortest path between two points in a simple polygon (with n vertices), without resorting to a (complicated) linear-time triangulation algorithm?" raised by J. S. B. Mitchell in Handbook of Computational Geometry (J. Sack and J. Urrutia, eds., Elsevier Science B.V., 2000), is still open. The aim of this paper is to show that convexity contributes to the design of efficient algorithms for solving some versions of shortest path problems (namely, computing the convex hull of a finite set of points and convex rope on rays in 2D, computing approximate shortest path between two points inside a simple polygon) without triangulation on the entire polygons. New algorithms are implemented in C and numerical examples are presented.

An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van



libCreme: An optimization library for evaluating convex-roof entanglement measures  

NASA Astrophysics Data System (ADS)

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the MATLAB programming language, but is fully compatible to the free and open-source OCTAVE platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focusing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems. Program summaryProgram title:libCreme Catalogue identifier: AEKD_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 3 No. of lines in distributed program, including test data, etc.: 4323 No. of bytes in distributed program, including test data, etc.: 70 542 Distribution format: tar.gz Programming language: Matlab/Octave and C/C++ Computer: All systems running Matlab or Octave Operating system: All systems running Matlab or Octave Classification: 4.9, 4.15 Nature of problem: Evaluate convex-roof entanglement measures. This involves solving a non-linear (unitary) optimization problem. Solution method: Two algorithms are provided: A conjugate-gradient method using a differential-geometric approach and a quasi-Newton method together with a mapping to Euclidean space. Running time: Typically seconds to minutes for a density matrix of a few low-dimensional systems and a decent implementation of the pure-state entanglement measure.

Röthlisberger, Beat; Lehmann, Jörg; Loss, Daniel




E-print Network

BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS Yenming M ABSTRACT Consider a sensing system using a large number of N microphones placed in multiple dimensions to monitor a broadband acoustic field. Using all the microphones at once is impractical because of the amount

Yorke, James


A Convex Optimization Approach to Modeling Consumer Heterogeneity in Conjoint Estimation  

Microsoft Academic Search

We propose and test a new approach for modeling consumer heterogeneity in conjoint estimation based on convex optimization and statistical machine learning. We develop methods both for metric and choice data. Like hierarchical Bayes (HB), our methods shrink individual-level partworth estimates towards a population mean. However, while HB samples from a posterior distribution that is influenced by exogenous parameters (the

Theodoros Evgeniou; Massimiliano Pontil; Olivier Toubia



On an Extension of Condition Number Theory to Non-Conic Convex Optimization  

E-print Network

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z* := minz ctx s.t. Ax - b Cy C Cx , to the more general non-conic format: z* := minx ctx ...

Freund, Robert M.


Convex Optimization: Fall 2013 Machine Learning 10-725/Statistics 36-725  

E-print Network

learning can be posed as optimization tasks that have special properties--such as convexity, smoothness topics: · Uses of duality, dual methods · Coordinate-based methods · Nonconvex methods · Large is The class schedule, lecture notes, homeworks, etc

Tibshirani, Ryan


A conic representation of the convex hull of disjunctive sets and conic cuts for integer second order cone optimization  

E-print Network

A conic representation of the convex hull of disjunctive sets and conic cuts for integer second No. (will be inserted by the editor) A conic representation of the convex hull of disjunctive sets and conic cuts for integer second order cone optimization Pietro Belotti · Julio C. G´oez · Imre P

Snyder, Larry


Cutting-Set Methods for Robust Convex Optimization with ...  

E-print Network

without any known distribution, and we choose a design whose worst-case ... cations includes robust control [31,32], robust portfolio optimization [33–36], robust ..... of course, be used as the starting point for a local optimization method. .... the authors give a convergence proof that can be applied here without much change.



A Faster Algorithm for Quasi-convex Integer Polynomial Optimization  

E-print Network

Jun 23, 2010 ... is the binary encoding length of a bound on that region with r ? ldO(n), ... Kannan improved Lenstra's algorithm for linear integer optimization by ...... Symposium on Symbolic and Algebraic Computation, pages 259–266. ACM.



1 Automatic Code Generation for Real-Time Convex Optimization  

E-print Network

family. We describe a preliminary implementation, built on the Python-based modeling framework CVXMOD.3.1 Adaptive filtering and equalization 16 1.3.2 Optimal order execution 17 1.3.3 Sliding window smoothing 18 1


Dominating Sets for Convex Functions with some Applications  

Microsoft Academic Search

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity.In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how

E. Carrizosa; J. B. G. Frenk



Dominating Sets for Convex Functions with Some Applications  

Microsoft Academic Search

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this paper, we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show

E. Carrizosa; J. B. G. Frenk



Exact Convex Relaxation of Optimal Power Flow in Radial Networks  

E-print Network

problems in power system operation since it was proposed in 1962 [1]. The OPF problem is increasingly important for distribution networks due to the advent of distributed generation (e.g., rooftop photovoltaic flow laws can be approximated by linear equations known as the DC power flow model [2]­[4], if 1) line

Low, Steven H.


Solving log-determinant optimization problems by a Newton-CG ...  

E-print Network

Sep 29, 2009 ... conjugate gradient solver. When applying the .... augmented Lagrangian methods for solving convex optimization problems including (P) and (D). ..... Note that the minimization problem in (13) is an unconstrained problem and the objective ..... ally, in our MATLAB code, one can optionally add this term.



Applications of convex optimization in signal processing and digital communication  

Microsoft Academic Search

In the last two decades, the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization. These advances have recently started to signifi- cantly impact various fields of applied sciences and engineering where computational efficiency is essential. This paper focuses on two such fields: digital signal processing and communication. In the past, the widely used

Zhi-Quan Luo



Templates for Convex Cone Problems with Applications to Sparse ...  

E-print Network

for which no efficient large-scale solvers exist, in a few hundred iterations. Finally ..... this cost to O(1/ .... lems, and common nuclear-norm minimization problems. ...... test image (Figure 8 (a)) which decay roughly according to a power law, and.



Convex optimization methods for graphs and statistical modeling  

E-print Network

An outstanding challenge in many problems throughout science and engineering is to succinctly characterize the relationships among a large number of interacting entities. Models based on graphs form one major thrust in ...

Chandrasekaran, Venkat



Solving convex (and linear) complementarity problems by projection methods (undamped Newton)  

SciTech Connect

A recent approach for solving the Linear Complementarity Problem (LCP) has been the solution of an equivalent system of piecewise linear equations through damped Newton methods. Since these functions are not everywhere differentiable, Newton methods have been adapted to deal with B-differentiable functions. The main drawback of this approach is the need to globalize the results by means of a step-size procedure. We adapt a new method of projections on certain convex sets to solve the LCP. This approach becomes a Newton method with no need of stepsize. Both the theoretical and practical implications are encouraging. The convergence conditions extend with no modifications to a more general convex complementarity problem. If the procedure converges to a nondegenerate solution, the usual Newton quadratic rate of convergence is achieved.

Garcia-Palomares, U.M.



Convex Approximations of Chance Constrained Programs  

E-print Network

Key words: stochastic programming, chance constraints, convex programming, ... Chance constrained optimization problems were introduced in Charnes et al ... Typically, the only way to estimate the probability for a chance constraint to be ...




E-print Network

in computer vision. Numerous prob- lems in this field as well as in image analysis and other branches, Global Optimaization in One Dimen- sional Vision, Submitted to SIAM Journal on Imaging Sciences. · C Squares Solutions for Qua- siconvex 1D vision Problems, Proc. Scandinavian Conference on Image Analysis

Lunds Universitet


The Power of Convex Relaxation: Near-Optimal Matrix Completion  

E-print Network

problem, and comes up in a great number of applications, including the famous Netflix Prize and other [7], and comes up in a great number of applications, including the famous Netflix Prize and other information from many users. Netflix is a commercial company implementing collaborative filtering, and seeks

Candes, Emmanuel J.


Satisfactory Efficient Linear Coordination Method forMulti-Objective Linear Programming Problems withConvex Polyhedral Preference Functions  

NASA Astrophysics Data System (ADS)

At present, the most commonly used satisficing method for multi-objective linear programming (MOLP) is the goal programming (GP) based method but this method does not always generate efficient solutions. Recently, an efficient GP-based method, which is called reference goal programming (RGP), has been proposed. However, it is limited to only a certain target point preference, which is too rigid. More flexible preferences such convex polyhedral preferences are preferred for many practical problems. In this research, a satisfactory effective linear coordination method for MOLP problems with convex polyhedral preference functions is proposed. The concept of the convex cone is used to formulate the convex polyhedral preference function and the existing lexicographic model of the reference point method (RPM) is integrated to ensure the efficiency of the solution of the problem. The formulated model can be solved by existing linear programming solvers and can find the satisfactory efficient solution. The convex polyhedral function enriches the existing preferences for efficient methods and increases the flexibility in designing preferences for decision makers. In some situation, it is difficult for a decision maker to state a certain desirable level for each objective function. Applying fuzzy goal to capture the decision maker’s preferences has the advantage of allowing for vague aspirations, which can be considered as convex polyhedral preference functions. The satisfactory efficient linear coordination method can be applied to obtain an efficient solution, which is also close to the decision maker’s requirements.

Phruksaphanrat, Busaba; Ohsato, Ario


About an Optimal Visiting Problem  

SciTech Connect

In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.

Bagagiolo, Fabio, E-mail:; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)



Optimization and geophysical inverse problems  

SciTech Connect

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 or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.

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.



Interval-Valued Optimization Problems Involving (?, ?)-Right Upper-Dini-Derivative Functions  

PubMed Central

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989



Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects.  


Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier. PMID:18941280

Hoffmann, Aswin L; den Hertog, Dick; Siem, Alex Y D; Kaanders, Johannes H A M; Huizenga, Henk



IEEE TRANS. ON CONTROL OF NETWORK SYSTEMS, JUNE 2014 (WITH PROOFS) 1 Convex Relaxation of Optimal Power Flow  

E-print Network

IEEE TRANS. ON CONTROL OF NETWORK SYSTEMS, JUNE 2014 (WITH PROOFS) 1 Convex Relaxation of Optimal Engineering and Applied Science, Caltech June 8, 2014 Abstract This tutorial summarizes, June 2014. This is an extended version with Appendex VI that proves the main results in this tutorial

Low, Steven H.


Locational optimization problems solved through Voronoi diagrams  

Microsoft Academic Search

This paper reviews a class of continuous locational optimization problems (where an optimal location or an optimal configuration of facilities is found in a continuum on a plane or a network) that can be solved through the Voronoi diagram. Eight types of continuous locational optimization problems are formulated, and these problems are solved through the ordinary Voronoi diagram, the farthest-point

Atsuyuki Okabe; Atsuo Suzuki



Approximating random quantum optimization problems  

NASA Astrophysics Data System (ADS)

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.

Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.



Prostate segmentation: an efficient convex optimization approach with axial symmetry using 3-D TRUS and MR images.  


We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers. PMID:24710163

Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron



VI. Convexity Convex sets  

E-print Network

to convex sets. The unit ball B as well as the closed unit ball B - in a nls X are convex since #(1 - #)x ** Let X ls. For any two x, y # X, we call [x . . y] := {(1 - #)x + #y : # # [0 . . 1]} the (closed of the unit ball in a nls plays an important role. In this chapter, IF = IR. ** convexity is local linearity

Liblit, Ben


A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces  

NASA Astrophysics Data System (ADS)

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.

Jin, Qinian; Lu, Xiliang



Cooperative optimal path planning for herding problems  

E-print Network

destination following weighted time-optimal and effort-optimal control paths. Simulation of this herding problem is accomplished through dynamic programming by utilizing the SNOPT software in the MATLAB environment. The numerical solution gives us the optimal...

Lu, Zhenyu



Tractable Approximations to Robust Conic Optimization Problems  

Microsoft Academic Search

In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semideflnite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal

Dimitris Bertsimas; Melvyn Sim



The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems  

Microsoft Academic Search

The planar Euclidean version of the traveling salesperson problem requires finding the shortest tour through a two-dimensional\\u000a array of points. MacGregor and Ormerod (1996) have suggested that people solve such problems by using a global-to-local perceptual\\u000a organizing process based on the convex hull of the array. We review evidence for and against this idea, before considering\\u000a an alternative, local-to-global perceptual

Douglas Vickers; Michael D. Lee; Matthew Dry; Peter Hughes



On Convex Relaxations for Quadratically Constrained Quadratic ...  

E-print Network

Jul 28, 2010 ... In the case that Qi ? 0 for each i, QCQP is a convex programming problem that can be solved ... QCQP is a fundamental problem that has been extensively studied in the global optimization literature; ..... In Table 1 we report the results of applying several increasingly tight ..... SIAM Review, 38:49–95,. 1996.



NP-hardness of deciding convexity of quartic polynomials and related problems  

E-print Network

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves ...

Ahmadi, Amir Ali


Two general methods for inverse optimization problems  

Microsoft Academic Search

We formulate a group of inverse optimization problems as a uniform LP model and provide two computation methods. One is a column generation method which generates necessary columns for simplex method by solving the original optimization problem. Another is an application of the ellipsoid method which can solve the group of inverse problems in polynomial time provided that the original

C. Yang; J. Zhang



Bucket elimination for multiobjective optimization problems  

Microsoft Academic Search

Multiobjective optimization deals with problems involving multiple measures of performance that should be optimized simultane- ously. In this paper we extend bucket elimination (BE), a well known dynamic programming generic algorithm, from mono-objective to multi- objective optimization. We show that the resulting algorithm, MO-BE, can be applied to true multi-objective problems as well as mono-objective problems with knapsack (or related)

Emma Rollon; Javier Larrosa



On implementing a primal-dual interior-point method for conic quadratic optimization  

Microsoft Academic Search

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an ane set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can in

Erling D. Andersen; Cornelis Roos; Tamás Terlaky



Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems  

NASA Astrophysics Data System (ADS)

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.

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao


Ant Colony Optimization and Hypergraph Covering Problems  

E-print Network

Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...

Pat, Ankit



On Identification of the Optimal Partition of Second Order Cone Optimization Problems  

E-print Network

[26] extends the concept of optimal partition to general convex conic optimization, and [3] provides for the general case. This paper is organized as follows. In Section 2, we review some key results for SOCO. In Section 3, after reviewing the definition of optimal partition for SOCO, we first propose two condition

Snyder, Larry


Local Optimization and the Traveling Salesman Problem  

Microsoft Academic Search

The Traveling Salesman Problem (TSP) is often cited as the prototypical hard combinatorial optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called local optimization. This paper surveys the state of

David S. Johnson



Models for optimal harvest with convex function of growth rate of a population  

SciTech Connect

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma 1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alga Chlorella.

Lyashenko, O.I.



Convex Formulations of Air Traffic Flow  

E-print Network

INVITED P A P E R Convex Formulations of Air Traffic Flow Optimization Problems A new technique using a Eulerian network model to describe air traffic flow. The evolution of traffic on each edge in the Oakland Air Route Traffic Control Center. Several computational aspects of the method are assessed


Representations in Problem Solving: A Case Study with Optimization Problems  

ERIC Educational Resources Information Center

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…

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose



Problem Solving through an Optimization Problem in Geometry  

ERIC Educational Resources Information Center

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…

Poon, Kin Keung; Wong, Hang-Chi



Convex Bayes decision theory  

Microsoft Academic Search

The basic concepts of Levi's epistemic utility theory and credal convexity are presented. Epistemic utility, in addition to penalizing error as is done with traditional Bayesian decision methodology, permits a unit of informational value to be distributed among the hypotheses of a decision problem. Convex Bayes decision theory retains the conditioning structure of probability-based inference, but addresses many of the

W. C. Stirling; D. R. Morrell



A note on integral-convexity in Banach spaces  

NASA Astrophysics Data System (ADS)

In the present paper we focus on a generalization of the notion of integral convexity. This concept, introduced in [J.Y. Wang, Y.M. Ma, The integral convexity of sets and functionals in Banach spaces, J. Math. Anal. Appl. 295 (2004) 211-224] by replacing, in the definition of classical notion of convexity, the sum by the integral, has interesting applications in optimal control problems. By using, instead of Bochner integral, a more general vector integral, that of Pettis, we obtain some results on integral-extreme points of subsets of a Banach space stronger than those given in [J.Y. Wang, Y.M. Ma, The integral convexity of sets and functionals in Banach spaces, J. Math. Anal. Appl. 295 (2004) 211-224]. Finally, a natural example coming from measure theory is included, in order to reflect the relationships between different kinds of integral convexity.

Satco, B.



Convex Formulations of Learning from Crowds  

NASA Astrophysics Data System (ADS)

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.

Kajino, Hiroshi; Kashima, Hisashi


Stochastic Linear Quadratic Optimal Control Problems  

SciTech Connect

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.

Chen, S. [Department of Mathematics, Zhejiang University, Hangzhou 310027 (China); Yong, J. [Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433 (China)



Solving constrained optimization problems with hybrid particle swarm optimization  

NASA Astrophysics Data System (ADS)

Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.

Zahara, Erwie; Hu, Chia-Hsin



Convergent relaxations of polynomial optimization problems with ...  

E-print Network

introduce a hierarchy of semidefinite programming relaxations which ... A standard problem in optimization theory is to find the global minimum of a ...... for K[x, x?]/I. Then we only need to consider polynomial expressions of the form q = ?.



Energy minimization for real-time systems with non-convex and discrete operation modes  

Microsoft Academic Search

We present an optimal methodology for dynamic voltage scheduling problem in the presence of realistic assumption such as leakage-power and intra-task overheads. Our contri- bution is an optimal algorithm for energy minimization that concurrently assumes the presence of (1) non-convex energy-speed models as opposed to previously studied convex models, (2) dis- crete set of operational modes (voltages) and (3) intra-task

Foad Dabiri; Alireza Vahdatpour; Miodrag Potkonjak; Majid Sarrafzadeh



Fast spectroscopic imaging using online optimal sparse k-space acquisition and projections onto convex sets reconstruction.  


Long acquisition times, low resolution, and voxel contamination are major difficulties in the application of magnetic resonance spectroscopic imaging (MRSI). To overcome these difficulties, an online-optimized acquisition of k-space, termed sequential forward array selection (SFAS), was developed to reduce acquisition time without sacrificing spatial resolution. A 2D proton MRSI region of interest (ROI) was defined from a scout image and used to create a region of support (ROS) image. The ROS was then used to optimize and obtain a subset of k-space (i.e., a subset of nonuniform phase encodings) and hence reduce the acquisition time for MRSI. Reconstruction and processing software was developed in-house to process and reconstruct MRSI using the projections onto convex sets method. Phantom and in vivo studies showed that good-quality MRS images are obtainable with an approximately 80% reduction of data acquisition time. The reduction of the acquisition time depends on the area ratio of ROS to FOV (i.e., the smaller the ratio, the greater the time reduction). It is also possible to obtain higher-resolution MRS images within a reasonable time using this approach. MRSI with a resolution of 64 x 64 is possible with the acquisition time of the same as 24 x 24 using the traditional full k-space method. PMID:16680731

Gao, Yun; Strakowski, Stephen M; Reeves, Stanley J; Hetherington, Hoby P; Chu, Wen-Jang; Lee, Jing-Huei



Model results of optimized convex shapes for a solar thermal rocket thruster  

SciTech Connect

A computational, 3-D model for evaluating the performance of solar thermal thrusters is under development. The model combines Monte-Carlo and ray-tracing techniques to follow the ray paths of concentrated solar radiation through an axially symmetric heat-exchanger surface for both convex and concave cavity shapes. The enthalpy of a propellant, typically hydrogen gas, increases as it flows over the outer surface of the absorber/exchanger cavity. Surface temperatures are determined by the requirement that the input radiant power to surface elements balance with the reradiated power and heat conducted to the propellant. The model uses tabulated forms of surface emissivity and gas enthalpy. Temperature profiles result by iteratively calculating surface and propellant temperatures until the solutions converge to stable values. The model provides a means to determine the effectiveness of incorporating a secondary concentrator into the heat-exchanger cavity. A secondary concentrator increases the amount of radiant energy entering the cavity. The model will be used to evaluate the data obtained from upcoming experiments. Characteristics of some absorber/exchanger cavity shapes combined with optionally attached conical secondary concentrators for various propellant flow rates are presented. In addition, shapes that recover some of the diffuse radiant energy which would otherwise not enter the secondary concentrator are considered.

Cartier, S.L. [Sparta Inc., Edwards AFB, CA (United States). Phillips Lab.



A new deterministic global optimization method for general twice-differentiable constrained nonlinear programming problems  

NASA Astrophysics Data System (ADS)

A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.

Park, Y. C.; Chang, M. H.; Lee, T.-Y.



Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems  

PubMed Central

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. PMID:24744685

Zhang, Xiaoling; Huang, Hong-Zhong; Wang, Zhonglai; Xu, Huanwei



Interaction prediction optimization in multidisciplinary design optimization problems.  


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. PMID:24744685

Meng, Debiao; Zhang, Xiaoling; Huang, Hong-Zhong; Wang, Zhonglai; Xu, Huanwei



Exact Matrix Completion via Convex Optimization Emmanuel J. Cand`es  

E-print Network

a sampling of its entries. · The Netflix problem. In the area of recommender systems, users submit ratings items. A special instance of this problem is the now famous Netflix problem [2]. Users (rows of the data would like to complete this matrix so that the vendor (here Netflix) might recommend titles that any

Xie, Yao


Evolutionary optimality in stochastic search problems  

PubMed Central

Optimal’ behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima. PMID:20335195

Preston, Mark D.; Pitchford, Jonathan W.; Wood, A. Jamie



Using convex envelopes to solve the interactive fixed-charge linear programming problem  

Microsoft Academic Search

In the well-known fixed-charge linear programming problem, it is assumed, for each activity, that the value of the fixed charge incurred when the level of the activity is positive does not depend upon which other activities, if any, are also undertaken at a positive level. However, we have encountered several practical problems where this assumption does not hold. In an

H. P. Benson; S. S. Erenguc



Analysis of the Optimal Relaxed Control to an Optimal Control Problem  

SciTech Connect

Relaxed controls are widely used to analyze the existence of optimal controls in the literature. Though there are many optimal control problems admitting no optimal control, rare examples were shown. This paper will solve a particular optimal control problem by analyzing the optimal relaxed controls, showing the ideas we used to study such kind of problems.

Lou Hongwei [Fudan University, School of Mathematical Sciences (China)], E-mail:



On the Convex Parameterization of Constrained Spacecraft Reorientation  

Microsoft Academic Search

Guiding the rotational motion of a spacecraft subject to constraints on its permissible orientation often leads to nonconvex optimal control problems. In this paper, we consider convex parameterizations of sets associated with the constrained rigid body orientations. We then elaborate on ramifications of such a parameterization in the development of steering laws for autonomous spacecraft reorientation that are based on

Yoonsoo Kim; Mehran Mesbahi; Gurkirpal Singh; Fred Y. Hadaegh



Exact Matrix Completion via Convex Optimization Emmanuel J. Cand`es  

E-print Network

would like to be able to recover a low-rank matrix from a sampling of its entries. · The Netflix problem is the now famous Netflix problem [2]. Users (rows of the data matrix) are given the opportunity to rate that the vendor (here Netflix) might recommend titles that any particular user is likely to be willing to order

Recht, Ben


Multiview stereo and silhouette consistency via convex functionals over convex domains.  


We propose a convex formulation for silhouette and stereo fusion in 3D reconstruction from multiple images. The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions. As a consequence, we can retain the original stereo-weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies, yet still obtain meaningful (non-empty) reconstructions which are guaranteed to be silhouette-consistent. We prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution. Compared to existing alternatives, the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets. We show that this projection can be solved exactly using an efficient algorithm. We propose a parallel implementation of the resulting convex optimization problem on a graphics card. Given a photo-consistency map and a set of image silhouettes, we are able to compute highly accurate and silhouette-consistent reconstructions for challenging real-world data sets. In particular, experimental results demonstrate that the proposed silhouette constraints help to preserve fine-scale details of the reconstructed shape. Computation times depend on the resolution of the input imagery and vary between a few seconds and a couple of minutes for all experiments in this paper. PMID:20820076

Cremers, Daniel; Kolev, Kalin



LDRD Final Report: Global Optimization for Engineering Science Problems  

SciTech Connect

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.




Optimal Planning and Problem-Solving  

NASA Technical Reports Server (NTRS)

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.

Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg



A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winners-take-all problem.  


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. PMID:19228555

Hu, Xiaolin; Zhang, Bo



Convex Optimization of Coincidence Time Resolution for a High-Resolution PET System  

Microsoft Academic Search

We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintilla- tors 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

Paul D. Reynolds; Peter D. Olcott; Guillem Pratx; Frances W. Y. Lau; Craig S. Levin



Optimization Online Digest -- August 2012  

E-print Network

A Newton-Fixed Point Homotopy Algorithm for Nonlinear Complementarity Problems with Generalized ... An adaptive accelerated first-order method for convex optimization ... Bounds for nested law invariant coherent risk measures. Linwei Xin ...


Optimal Control of an Obstacle Problem Maitine Bergounioux  

E-print Network

control problems governed by variational inequalities. and more precisely the obstacle problem. Since we the control and the state. Our purpose is to give some optimality conditions that can be easily exploited-Puel [11]. Then, we consider the optimal control problem as a "stan- dard" control problem governed

Paris-Sud XI, Université de


Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspond- ing inverse optimization problem is to nd a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods

Clemens Heuberger



Inverse Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspondinginverse optimization problem is to nd a minimal adjustment of the parameters of theproblem (costs, capacities, . . . ) such that the given solution becomes optimum.Several such problems have been studied in the last ten years. After formalizing the notionof an inverse problem and its variants, we

Clemens Heuberger



Pathwise coordinate optimization  

Microsoft Academic Search

We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with the

Jerome Friedman; Trevor Hastie; Holger Höfling; Robert Tibshirani



Optimal shape design as a material distribution problem  

Microsoft Academic Search

Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a

M. P. Bendsře



Robust Conic Quadratic and Semidefinite Optimization  

E-print Network

Lecture 3 Robust Conic Quadratic and Semidefinite Optimization In this lecture, we extend the RO methodology onto non-linear convex optimization problems, specifically, conic ones. 3.1 Uncertain Conic Optimization: Preliminaries 3.1.1 Conic Programs A conic optimization (CO) problem (also called conic program

Nemirovski, Arkadi


Fast Approximate Convex Decomposition  

E-print Network

Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...

Ghosh, Mukulika



FRANOPP: Framework for analysis and optimization problems user's guide  

NASA Technical Reports Server (NTRS)

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.

Riley, K. M.



Investigation of Particle Swarm Optimization for Job Shop Scheduling Problem  

Microsoft Academic Search

Job shop scheduling problem has stronger processing constraints, and it is a kind of well-known combination optimization problem. Particle swarm optimization algorithm is employed to solve the job shop scheduling problem, and the objective is minimizing the maximum completion time of all the jobs. The particle representation based on operation-particle position sequence is proposed. In the particle representation, the mapping

Zhixiong Liu



Numerical methods for solving applied optimal control problems  

NASA Astrophysics Data System (ADS)

For an optimal control problem with state constraints, an iterative solution method is described based on reduction to a finite-dimensional problem, followed by applying a successive linearization algorithm with the use of an augmented Lagrangian. The efficiency of taking into account state constraints in optimal control computation is illustrated by numerically solving several application problems.

Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.



Algorithm for the Optimal Riding Scheme Problem in Public traffic  

Microsoft Academic Search

A two-stage algorithm is proposed for the optimal riding scheme problem in public traffic querying system. The first stage is to find out the least transfer schemes, in which bus line network model is presented to convert the least transfer scheme problem into the shortest path problem. The second stage is to search out the optimal riding scheme from the

Dong Jiyang; Chen Luzhuo



Some optimization problems in power system reliability analysis  

E-print Network

This dissertation aims to address two optimization problems involving power system reliabilty analysis, namely multi-area power system adequacy planning and transformer maintenance optimization. A new simulation method for power system reliability...

Jirutitijaroen, Panida



Problem Decomposition and MultiObjective Optimization Richard A. Watson  

E-print Network

Problem Decomposition and Multi­Objective Optimization Richard A. Watson Dynamical and Evolutionary and designing the body. It is acknowledged that most real­world prob­ lems (vehicles included) do not decompose. In problem decomposition we think of a problem with multiple sub­problems, in MOO we think of a problem

Coello, Carlos A. Coello


Nonlinear Approach to a Class of Combinatorial Optimization Problems.  

National Technical Information Service (NTIS)

A special class of combinatorial optimization problems is considered. The authors develop a compact nonconvex quadratic model for these problems that incorporates all inequality constraints in the objective function, and discuss two algorithms for solving...

J. P. Warners



Optimization Online - Integer Programming Submissions - 2012  

E-print Network

A conic representation of the convex hull of disjunctive sets and conic cuts for integer ... Two-stage Models and Algorithms for Optimizing Infrastructure Design and ... Solving mixed integer nonlinear programming problems for mine production ...


An Ant Colony Optimization Algorithm for Shop Scheduling Problems  

Microsoft Academic Search

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure

Christian Blum; Michael Sampels



An new efficient evolutionary approach for dynamic optimization problems  

Microsoft Academic Search

To improve the efficiency of the currently known evolutionary algorithms for dynamic optimization problems, we have proposed a novel variable representation allows static evolutionary optimization approaches to be extended to efficiently explore global and better local optimal areas in dynamic fitness landscapes. It represents a single individual as three real-valued vectors (x,ż,r)ż Rn ?? Rn ?? R2 in the evolutionary

Yong Liang



Improved Genetic Algorithms to Solving Constrained Optimization Problems  

Microsoft Academic Search

The slow convergence speed and the lack of effective constraint handling strategies are the major concerns when applying genetic algorithms (Gas) to constrained optimization problem. An improved genetic algorithm was proposed by dividing population into three parts: optimal subpopulation, elitists subpopulation and spare subpopulation. We applied genetic algorithm on three subpopulations with different evolutionary strategies. Isolation of optimal subpopulation was

Zhu Can; Liang Xi-Ming; Zhou Shu-renhu



The Traveling Salesman Problem: A Case Study in Local Optimization  

Microsoft Academic Search

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including clas- sical local optimization techniques as well

David S. Johnson; Lyle A. McGeoch


Enumerating Optimal Solutions to Special Instances of the Lottery Problem  

E-print Network

Enumerating Optimal Solutions to Special Instances of the Lottery Problem AP Burger # & JH van�isomorphic optimal lottery sets of cardinality three. We also determine numerically the number of non� isomorphic optimal playing sets for lotteries in which a single correct number is required to win a prize. Keywords

van Vuuren, Jan H.


Enumerating Optimal Solutions to Special Instances of the Lottery Problem  

E-print Network

Enumerating Optimal Solutions to Special Instances of the Lottery Problem AP Burger & JH van Vuuren-isomorphic optimal lottery sets of cardinality three. We also determine numerically the number of non- isomorphic optimal playing sets for lotteries in which a single correct number is required to win a prize. Keywords

van Vuuren, Jan H.


A planning problem combining calculus of variations and optimal transport  

E-print Network

/assignment problems have their modern roots in planning prob- lems (optimally transporting coal from mines to steel to most skilled workers). It is however reasonable to think that, in addition to designing and will compare them. The coupled problem thus amounts to solve a standard optimal transport where the cost

Lachapelle, Aimé


Hybrid particle swarm optimization and convergence analysis for scheduling problems  

Microsoft Academic Search

This paper proposes a hybrid particle swarm optimization algorithm and for solving Flow Shop Scheduling Problems (FSSP) and Job Shop Scheduling Problems (JSSP) to minimize the maximum makespan. A new hybrid heuristic, based on Particle Swarm Optimization (PSO), Tabu Search (TS) and Simulated Annealing (SA), is presented. By reasonably combining these three different search algorithms, we develop a robust, fast

Xue-Feng Zhang; Miyuki Koshimura; Hiroshi Fujita; Ryuzo Hasegawa



Alternative Solutions for Optimization Problems in Generalizability Theory.  

ERIC Educational Resources Information Center

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…

Sanders, Piet F.



Branch-and-Cut Algorithms for Combinatorial Optimization Problems1  

E-print Network

Branch-and-Cut Algorithms for Combinatorial Optimization Problems1 John E. Mitchell2 Mathematical of optimality. We describe how a branch-and-cut method can be tailored to a specific integer programming problem:// April 19, 1999, revised September 7, 1999. Abstract Branch-and-cut methods are very successful

Mitchell, John E.


BranchandCut Algorithms for Combinatorial Optimization Problems 1  

E-print Network

Branch­and­Cut Algorithms for Combinatorial Optimization Problems 1 John E. Mitchell 2 Mathematical of optimality. We describe how a branch­and­cut method can be tailored to a specific integer programming problem://�mitchj April 19, 1999, revised September 7, 1999. Abstract Branch­and­cut methods are very successful

Mitchell, John E.


Multiobjective particle swarm optimization for environmental\\/economic dispatch problem  

Microsoft Academic Search

A new multiobjective particle swarm optimization (MOPSO) technique for environmental\\/economic dispatch (EED) problem is proposed in this paper. The proposed MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of global best and local best individuals in multiobjective optimization domain. The proposed MOPSO technique has been implemented to solve the EED problem with competing and non-commensurable cost and

M. A. Abido



Problems in large-scale structural optimization  

NASA Technical Reports Server (NTRS)

A general design optimization model for large complex systems is defined. Major features of the model that challenge various optimization algorithms are discussed. Requirements of a model optimization algorithm are identified. Objectives of the study of various algorithms are defined and a basis for conducting such a study is developed. Primal as well as transformation methods are analytically studied and a unified viewpoint of various methods is presented. Several numerical examples are solved using different methods to study their performance. Conclusions drawn from the study are presented and discussed. Areas of future research in nonlinear programming as well as structural optimization are identified and discussed.

Arora, J. S.; Belegundu, A. D.



Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems  

NASA Technical Reports Server (NTRS)

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.

Balling, R. J.; Wilkinson, C. A.



Motivation Optimization scheme The problem Running conditions Tools Experiments Conclusions Optimizing the execution of a parallel meteorology  

E-print Network

Motivation Optimization scheme The problem Running conditions Tools Experiments Conclusions 2009 #12;Motivation Optimization scheme The problem Running conditions Tools Experiments Conclusions Contents 1 Motivation 2 Optimization scheme 3 The problem 4 Running conditions 5 Tools 6 Experiments 7

Giménez, Domingo


Some Optimization Problems for p-Laplacian Type Equations  

SciTech Connect

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional over some admissible class of loads f where u is the (unique) solution to the problem -{delta}{sub p}u+ vertical bar u vertical bar {sup p-2}u=0 in {omega} with vertical bar {nabla}u vertical bar {sup p-2}u{sub {nu}}=f on {partial_derivative}{omega}.

Del Pezzo, L. M., E-mail:; Fernandez Bonder, J. [Universidad de Buenos Aires, Departamento de Matematica, FCEyN (Argentina)], E-mail:




PubMed Central

In this paper, we study several interesting optimal-ratio region detection (ORD) problems in d-D (d ? 3) discrete geometric spaces, which arise in high dimensional medical image segmentation. Given a d-D voxel grid of n cells, two classes of geometric regions that are enclosed by a single or two coupled smooth heighfield surfaces defined on the entire grid domain are considered. The objective functions are normalized by a function of the desired regions, which avoids a bias to produce an overly large or small region resulting from data noise. The normalization functions that we employ are used in real medical image segmentation. To our best knowledge, no previous results on these problems in high dimensions are known. We develop a unified algorithmic framework based on a careful characterization of the intrinsic geometric structures and a nontrivial graph transformation scheme, yielding efficient polynomial time algorithms for solving these ORD problems. Our main ideas include the following. We observe that the optimal solution to the ORD problems can be obtained via the construction of a convex hull for a set of O(n) unknown 2-D points using the hand probing technique. The probing oracles are implemented by computing a minimum s-t cut in a weighted directed graph. The ORD problems are then solved by O(n) calls to the minimum s-t cut algorithm. For the class of regions bounded by a single heighfield surface, our further investigation shows that the O(n) calls to the minimum s-t cut algorithm are on a monotone parametric flow network, which enables to detect the optimal-ratio region in the complexity of computing a single maximum flow.

Wu, Xiaodong



Metaheuristic Optimization: Algorithm Analysis and Open Problems  

Microsoft Academic Search

\\u000a Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have\\u000a emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular.\\u000a Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved\\u000a for the majority of metaheuristic algorithms, while efficiency analysis is

Xin-She Yang



Nonlinear Conic Optimization --why and how--  

E-print Network

Nonlinear Conic Optimization --why and how-- Michal Kocvara School of Mathematics, The University Optimization 1 / 38 #12;Conic optimization "generalized" mathematical optimization problem min f(x) subject to gi(x) Ki, i = 1, . . . , m Ki -- convex cone Rni , ni n f, gi -- linear linear conic

Sidorov, Nikita


A Planning Problem Combining Calculus of Variations and Optimal Transport  

SciTech Connect

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.

Carlier, G., E-mail:; Lachapelle, A., E-mail: lachapelle@ceremade.dauphine.f [Universite Paris IX Dauphine, CEREMADE, UMR CNRS 7534 (France)



Optimal solutions for a free boundary problem for crystal growth  

E-print Network

Optimal solutions for a free boundary problem for crystal growth Pekka Neittaanm¨ aki Thomas I. Seidman Abstract. We consider a free boundary problem modeling the growth/dissolution of a crystal boundary problem corresponding to a model of growth (dissolution) of a radially symmetric crystal grain

Seidman, Thomas I.


Optimal boundary control problems related to high-lift configurations  

E-print Network

Optimal boundary control problems related to high-lift configurations Christian John, Bernd R problems related to the aerodynamic optimiza- tion of flows around airfoils in high-lift configurations, 25]. Our paper deals with two problems, both related to high-lift configurations, where the lift

Tröltzsch, Fredi


An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems.  


We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art. PMID:20840899

Afonso, Manya V; Bioucas-Dias, José M; Figueiredo, Mário A T



Unified Particle Swarm Optimization for Solving Constrained Engineering Optimization Problems  

E-print Network

and the algorithm is modified to preserve feasibility of the encountered solutions. The algorithm is illustrated efficiently and effectively. Due to the nature of these applications, the solutions usually need. On the other hand, stochastic optimization algorithms such as Genetic Algorithms, Evolution Strategies

Parsopoulos, Konstantinos


Robust stability and contraction analysis of nonlinear systems via semidefinite optimization  

E-print Network

A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These ...

Aylward, Erin M



Applications of parallel global optimization to mechanics problems  

NASA Astrophysics Data System (ADS)

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.

Schutte, Jaco Francois


Multiple local minima in radiotherapy optimization problems with dose-volume constraints.  


The cause of multiple local minima in beam weight optimization problems subject to dose-volume constraints is analyzed. Three objective functions were considered: (a) maximization of tumor control probability (TCP), (b) maximization of the minimum target dose, and (c) minimization of the mean-squared-deviation of the target dose from the prescription dose. It is shown that: (a) TCP models generally result in strongly quasiconvex objective functions; (b) maximization of the minimum target dose results in a strongly quasiconvex objective function; and (c) minimizing the root-mean-square dose deviation results in a convex objective function. Dose-volume constraints are considered such that, for each region at risk (RAR), the volume of tissue whose dose exceeds a certain tolerance dose (DTol) is kept equal to or below a given fractional level (VTol). If all RARs lack a "volume effect" (i.e., VTol = 0 for all RARs) then there is a single local minimum. But if volume effects are present, then the feasible space is possibly nonconvex and therefore possibly leads to multiple local minima. These conclusions hold for all three objective functions. Hence, possible local minima come not from the nonlinear nature of the objective functions considered, but from the "either this volume or that volume but not both" nature of the volume effect. These observations imply that optimization algorithms for dose-volume constraint types of problems should have effective strategies for dealing with multiple local minima. PMID:9243478

Deasy, J O



Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution  

Microsoft Academic Search

We concentrate here on decomposition of 2D objects into mean- ingful parts of visual form ,o rvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identify- ing convex parts at

Longin Jan Latecki; Rolf Lakämper



Comparison of optimal design methods in inverse problems  

NASA Astrophysics Data System (ADS)

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).

Banks, H. T.; Holm, K.; Kappel, F.



Optimal control problems in public health  

Microsoft Academic Search

The health care delivery system in the United States is poorly planned to meet the growing needs of its population. This research establishes the foundations of developing decision-support tools in the emerging field of health care engineering, with special emphasis on public health. It demonstrates the potential of applying engineering methods, especially optimal control theory, to facilitate decision making in

Feng Lin



A cavity approach to optimization and inverse dynamical problems  

E-print Network

In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in irreversible dynamical processes. These two classes of problems are formally very similar: they both require an efficient procedure to trace over all trajectories of either auxiliary variables which enforce global constraints, or directly dynamical variables defining the inverse dynamical problems. We will mention three basic examples, namely the Minimum Steiner Tree problem, the inverse threshold linear dynamical problem, and the zero patient problem in epidemic cascades. All these examples are root problems in optimization and inference over networks. They appear in many modern applications and in a variety of different contexts. Credit for these results should be shared with A. Braunstein, A. Ramezanpour, F. Altarelli, L. Dall'Asta, and A. Lage-Castellanos.

Lage-Castellanos, Alejandro; Zecchina, Riccardo



Direct Multiple Shooting Optimization with Variable Problem Parameters  

NASA Technical Reports Server (NTRS)

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.

Whitley, Ryan J.; Ocampo, Cesar A.



Decomposition methods for large scale stochastic and robust optimization problems  

E-print Network

We propose new decomposition methods for use on broad families of stochastic and robust optimization problems in order to yield tractable approaches for large-scale real world application. We introduce a new type of a ...

Becker, Adrian Bernard Druke



PLASMA Approximate Dynamic Programming finally cracks the locomotive optimization problem  

E-print Network

PLASMA ­ Approximate Dynamic Programming finally cracks the locomotive optimization problem schedules and new operating policies. PLASMA is currently running at Norfolk Southern for strategic of PLASMA: Each locomotive is modeled individually, making it possible to capture both horsepower

Powell, Warren B.


Infinite-horizon optimal control problems in economics  

NASA Astrophysics Data System (ADS)

This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.

Aseev, Sergei M.; Besov, Konstantin O.; Kryazhimskii, Arkadii V.



The tracial moment problem and trace-optimization of polynomials  

E-print Network

conjecture [BMV75] from statistical quantum mechanics. .... truncated tracial moment problem, like in the classical case of polynomial optimization on Rn ...... Positive polynomials in control, volume 312 of Lecture Notes in Control and Inform.



Maximum-Demand Rectangular Location Problem - Optimization ...  

E-print Network

MDRLP is the problem of positioning a given number of rectangular service zones ... Applications of MDRLP range from classical facility location for providing ... Citation: Report# MBKK2, Department of Industrial and Systems Engineering, ...

Manish Bansal


Convoy Movement Problem – An Optimization Perspective  

Microsoft Academic Search

\\u000a This chapter addresses the convoy movement problem (CMP) in military logistics. CMP involves routing and scheduling military\\u000a convoys within the strategic constraints. The chapter begins with an introduction to the domain of military logistics. It\\u000a is followed by formal specification of CMP, computational complexity and classification of the problem. Section 2 highlights\\u000a the state of art as is evident from

P. N. Ram Kumar; T. T. Narendran


Optimal Policies for a Multi-Echelon Inventory Problem  

Microsoft Academic Search

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment

Andrew J. Clark; Herbert Scarf




E-print Network

problems; existence of optimal solutions; iterative computational meth- ods; gradient methods - motivation direction methods; the conjugate gradient method; quasi-Newton methods of Davidon- Fletcher-Powell (DFP Reference: , MATLAB Optimization Toolbox User's Guide. Natick, MA: MathWorks, 1990-2008. http://www

Southern California, University of


On Free Surface PDE Constrained Shape Optimization Problem  

E-print Network

. Such problems are inspired by the process of continuous casting of steel where optimization of large vortex of such processes are coating flows [15], thin film manufacturing processes [24], and continuous casting of steel demands related to quality of steel products, optimization of processes involved in continuous casting

Kunisch, Karl


Finding Optimal Gains In Linear-Quadratic Control Problems  

NASA Technical Reports Server (NTRS)

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Milman, Mark H.; Scheid, Robert E., Jr.



Some Finance Problems Solved with Nonsmooth Optimization Techniques  

E-print Network

Some Finance Problems Solved with Nonsmooth Optimization Techniques R. B. VINTER 1 AND H. ZHENG 2 analysis and mathematical finance communities to the scope for applications of nonsmooth optimization to finance, by studying in detail two illustrative examples. The first concerns the maximization of a ter

Vinter, Richard


An Integrated Optimizing-Simulator for the Military Airlift Problem  

Microsoft Academic Search

Abstract There have been two primary modeling and algorithmic strategies for problems in military logistics: simulation, oering tremendous modeling flexibility, and optimization, which oers the intelligence of math programming. Each oers,significant theoretical and practical advantages. In this paper, we use the framework of approximate dynamic programming which produces a form of “optimizing- simulator” which oers,a spectrum of models and algorithms

Tongqiang Tony Wu



A Complete Characterization of Complexity for Boolean Constraint Optimization Problems  

Microsoft Academic Search

\\u000a We analyze the complexity of optimization problems expressed using valued constraints. This very general framework includes\\u000a a number of well-known optimization problems such as MAX-SAT, and Weighted MAX-SAT, as well as properly generalizing the classical CSP framework by allowing the expression of preferences. We focus on valued\\u000a constraints over Boolean variables, and we establish a dichotomy theorem which characterizes the

David A. Cohen; Martin C. Cooper; Peter Jeavons



An Inverse Optimality Method to Solve a Class of Optimal Control Problems  

E-print Network

for a class of nonlinear systems. The main motivation for this work comes from the controller designer's perspective. When designers are faced with a control engineering problem and want to formulateAn Inverse Optimality Method to Solve a Class of Optimal Control Problems Luis Rodrigues1 , Didier

Henrion, Didier


An efficient algorithm for the earliness-tardiness scheduling problem  

E-print Network

Sep 7, 2005 ... jobs and that can solve problems with even more general non-convex cost functions. The ... Fry et al. [12] who proposed algorithms viable for 20 and 25 jobs respectively. ......, October 2004.



A D.C. optimization method for single facility location problems  

Microsoft Academic Search

The single facility location problem with general attraction and repulsion functions is considered. An algorithm based on a representation of the objective function as the difference of two convex (d.c.) functions is proposed. Convergence to a global solution of the problem is proven and extensive computational experience with an implementation of the procedure is reported for up to 100,000 points.

Hoang Tuy; Faiz Al-Khayyal; Fangjun Zhou



Chapter 4: Unconstrained Optimization Unconstrained optimization problem minx F(x) or maxx F(x)  

E-print Network

Chapter 4: Unconstrained Optimization · Unconstrained optimization problem minx F(x) or maxx F(x) · Constrained optimization problem min x F(x) or max x F(x) subject to g(x) = 0 and/or h(x) x) > 0 Example: minimize the outer area of a cylinder subject to a fixed volume. Objective function F(x) = 2r2

Wu, Xiaolin


Fundamental differences between optimization code test problems in engineering applications  

NASA Technical Reports Server (NTRS)

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Eason, E. D.




E-print Network

A CLASS OF OPTIMAL TWO-DIMENSIONAL MULTIMATERIAL CONDUCTING LAMINATES NATHAN ALBIN1, ANDREJ, polyconvexity, rank-one convexity, multiwell variational problem . 1 #12;2 N. ALBIN, A. CHERKAEV, AND V. NESI

Cherkaev, Andrej


Forecasting Electricity Prices in an Optimization Hydrothermal Problem  

NASA Astrophysics Data System (ADS)

This paper presents an economic dispatch algorithm in a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of one firm is described, whose objective function can be defined as its profit maximization. Since next-day price forecasting is an aspect crucial, this paper proposes an efficient yet highly accurate next-day price new forecasting method using a functional time series approach trying to exploit the daily seasonal structure of the series of prices. For the optimization problem, an optimal control technique is applied and Pontryagin's theorem is employed.

Matías, J. M.; Bayón, L.; Suárez, P.; Argüelles, A.; Taboada, J.



Aircraft maintenance jacking problem via optimization  

Microsoft Academic Search

We address the problem of assigning forces to jacking positions in order to weaken stress at points where an aircraft maintenance operation has to be performed. We introduce a mixed-integer linear programming model and report encouraging computational experiments on historical data. Our methodology is currently under the process of industrial implementation at Airbus, where it will be used as a




Good solution for multi-objective optimization problem  

NASA Astrophysics Data System (ADS)

Multi-objective optimization problems have been solved widely by determination of a Pareto optimal set. Practically, the decision-makers need to choose only one solution to implement on their system, which is a challenge for them especially when the number of solutions in the Pareto set is large. In this paper, new method has been proposed to get a good solution for multi-objective optimization problem. The method consists of two stages; the first stage used the Multi Objective Simulated Annealing algorithm to find the Pareto set that contains the non-dominated solutions, whereas the second stage used the optimal computing allocation technique to reduce the number of solutions in the Pareto set to one solution that depends on ranking the preferences of the objective functions. To validate this method, multi-objective 01 knapsack problem was analyzed.

Abubaker, Ahmad; Baharum, Adam; Alrefaei, Mahmoud



Genetic Programming: Optimal Population Sizes for Varying Complexity Problems  

E-print Network

Genetic Programming: Optimal Population Sizes for Varying Complexity Problems Alan Piszcz and the ability to successfully evolve solutions. We find that population size sensitivity how much a genetic complex a problem is the more sensitive the genetic program's efficiency is to population size. Categories

Fernandez, Thomas


Biogeography-Based Optimization for the Traveling Salesman Problems  

Microsoft Academic Search

Biogeography-based optimization (BBO) is a novel evolutionary algorithm that is based on the mathematics of biogeography. In the BBO model, problem solutions are represented as islands, and the sharing of features between solutions is represented as immigration and emigration between the islands. This paper presents an application of the BBO algorithm to the traveling salesman problems. The BBO solution is

Ying Song; Min Liu; Zheng Wang



Optimal network problem: a branch-and-bound algorithm  

Microsoft Academic Search

The problem of selecting a subset of links so as to minimize the sum of shortest path distances between all pairs of nodes, subject to a budget constraint on total length of links, may be solved by a modification of a branch-and-bound algorithm developed for optimal variable selection problems in statistics. The modified algorithm is described in detail, and encouraging

D E Boyce; A Farhi; R Weischedel



NEOS and Condor: solving optimization problems over the Internet  

Microsoft Academic Search

We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations

Michael C. Ferris; Michael P. Mesnier; Jorge J. Moré



A behavioral approach to the H ? optimal control problem  

Microsoft Academic Search

This paper considers the general H? optimal control problem from a behavioral perspective. A formalization of this problem is given that departs from the usual H? control paradigm in the sense that system variables of the plant are treated in a symmetric way, without distinguishing control inputs, measurements, exogenous inputs and to-be-controlled variables. Interconnection variables are introduced and controllers are

Siep Weiland; Anton A. Stoorvogel; Bram de Jager



Solving inverse problems of identification type by optimal control methods  

SciTech Connect

Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations.

Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States); Jiongmin Yong [Fudan Univ., Shanghai (China). Mathematics Dept.



Application of probabilistic ordinal optimization concepts to a continuous-variable probabilistic optimization problem.  

SciTech Connect

A very general and robust approach to solving optimization problems involving probabilistic uncertainty is through the use of Probabilistic Ordinal Optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the probabilistic merits of local design alternatives, rather than on crisp quantification of the alternatives. Thus, we simply ask the question: 'Is that alternative better or worse than this one?' to some level of statistical confidence we require, not: 'HOW MUCH better or worse is that alternative to this one?'. In this paper we illustrate an elementary application of probabilistic ordinal concepts in a 2-D optimization problem. Two uncertain variables contribute to uncertainty in the response function. We use a simple Coordinate Pattern Search non-gradient-based optimizer to step toward the statistical optimum in the design space. We also discuss more sophisticated implementations, and some of the advantages and disadvantages versus non-ordinal approaches for optimization under uncertainty.

Romero, Vicente Jose; Ayon, Douglas V.; Chen, Chun-Hung (George Mason University, Fairfax, VA)



Solving Steiner tree problems in graphs to optimality  

Microsoft Academic Search

Abstract: In this paper, we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems,in graphs. Our algorithm,is based,on an integer programming,formulation,for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nearly all problem instances discussed in the literature to optimality, including one problem that—to our knowledge—has,not yet been,solved. We also report

Thorsten Koch; Alexander Martin



Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem  

Microsoft Academic Search

Robust design optimization (RDO) problems can generally be formulated by incorporating uncertainty into the corresponding\\u000a deterministic problems. In this context, a careful formulation of deterministic equality constraints into the robust domain\\u000a is necessary to avoid infeasible designs under uncertain conditions. The challenge of formulating equality constraints is\\u000a compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the

S. Rangavajhala; A. A. Mullur; A. Messac



Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems  

NASA Technical Reports Server (NTRS)

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.

Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.



Unified Solution to Nonnegative Data Factorization Problems  

Microsoft Academic Search

In this paper, we restudy the non-convex data factorization problems (regularized or not, unsupervised or supervised), where the optimization is confined in the nonnegative orthant, and provide a unified convergency provable solution based on multiplicative nonnegative update rules. This solution is general for optimization problems with block-wisely quadratic objective functions, and thus direct update rules can be derived by skipping

Xiaobai Liu; Shuicheng Yan; Jun Yan; Hai Jin



Efficient robust optimization for robust control with constraints  

Microsoft Academic Search

This paper proposes an ecien t computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterise this problem

Paul J. Goulart; Eric C. Kerrigan; Daniel Ralph



Ecien t Robust Optimization for Robust Control with Constraints  

Microsoft Academic Search

This paper proposes an ecien t computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem

Paul J. Goulart; Eric C. Kerrigan; Daniel Ralph


Climate Intervention as an Optimization Problem  

NASA Astrophysics Data System (ADS)

Typically, climate models simulations of intentional intervention in the climate system have taken the approach of imposing a change (eg, in solar flux, aerosol concentrations, aerosol emissions) and then predicting how that imposed change might affect Earth's climate or chemistry. Computations proceed from cause to effect. However, humans often proceed from "What do I want?" to "How do I get it?" One approach to thinking about intentional intervention in the climate system ("geoengineering") is to ask "What kind of climate do we want?" and then ask "What pattern of radiative forcing would come closest to achieving that desired climate state?" This involves defining climate goals and a cost function that measures how closely those goals are attained. (An important next step is to ask "How would we go about producing these desired patterns of radiative forcing?" However, this question is beyond the scope of our present study.) We performed a variety of climate simulations in NCAR's CAM3.1 atmospheric general circulation model with a slab ocean model and thermodynamic sea ice model. We then evaluated, for a specific set of climate forcing basis functions (ie, aerosol concentration distributions), the extent to which the climate response to a linear combination of those basis functions was similar to a linear combination of the climate response to each basis function taken individually. We then developed several cost functions (eg, relative to the 1xCO2 climate, minimize rms difference in zonal and annual mean land temperature, minimize rms difference in zonal and annual mean runoff, minimize rms difference in a combination of these temperature and runoff indices) and then predicted optimal combinations of our basis functions that would minimize these cost functions. Lastly, we produced forward simulations of the predicted optimal radiative forcing patterns and compared these with our expected results. Obviously, our climate model is much simpler than reality and predictions from individual models do not provide a sound basis for action; nevertheless, our model results indicate that the general approach outlined here can lead to patterns of radiative forcing that make the zonal annual mean climate of a high CO2 world markedly more similar to that of a low CO2 world simultaneously for both temperature and hydrological indices, where degree of similarity is measured using our explicit cost functions. We restricted ourselves to zonally uniform aerosol concentrations distributions that can be defined in terms of a positive-definite quadratic equation on the sine of latitude. Under this constraint, applying an aerosol distribution in a 2xCO2 climate that minimized a combination of rms difference in zonal and annual mean land temperature and runoff relative to the 1xCO2 climate, the rms difference in zonal and annual mean temperatures was reduced by ~90% and the rms difference in zonal and annual mean runoff was reduced by ~80%. This indicates that there may be potential for stratospheric aerosols to diminish simultaneously both temperature and hydrological cycle changes caused by excess CO2 in the atmosphere. Clearly, our model does not include many factors (eg, socio-political consequences, chemical consequences, ocean circulation changes, aerosol transport and microphysics) so we do not argue strongly for our specific climate model results, however, we do argue strongly in favor of our methodological approach. The proposed approach is general, in the sense that cost functions can be developed that represent different valuations. While the choice of appropriate cost functions is inherently a value judgment, evaluating those functions for a specific climate simulation is a quantitative exercise. Thus, the use of explicit cost functions in evaluating model results for climate intervention scenarios is a clear way of separating value judgments from purely scientific and technical issues.

Caldeira, Ken; Ban-Weiss, George A.



A generalization of the Chandler Davis convexity theorem  

Microsoft Academic Search

In 1957 Chandler Davis proved a theorem that a rotationally invariant function on symmetric matrices is convex if and only if it is convex on the diagonal matrices. We generalize this result to groups acting nonlinearly on convex subsets of arbitrary vector spaces thereby understanding the abstract mechanism behind the classical theorem. We apply the new theorem to a problem

Yury Grabovsky; Omar Hijab



Russian Doll Search for solving Constraint Optimization problems  

SciTech Connect

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.

Verfaillie, G.; Lemaitre, M. [CERT/ONERA, Toulouse (France); Schiex, T. [INRA, Castanet Tolosan (France)



Optimization of fully coupled electrostatic–fluid–structure interaction problems  

Microsoft Academic Search

A formal methodology is presented for high fidelity analysis and design optimization of structures undergoing electrostatic–fluid–structure interaction. The optimization problem is solved by gradient-based algorithms. A five-field formulation of the fully coupled electrostatic–fluid–structure system is presented. Based on this formulation, the coupled global sensitivity equations are derived. The analysis and sensitivity analysis are both solved by staggered procedures. The presented

Michael Raulli; Kurt Maute



Space-mapping optimization of microwave circuits exploiting surrogate models  

Microsoft Academic Search

A powerful new space-mapping (SM) optimization algorithm is presented in this paper. It draws upon recent developments in both surrogate model-based optimization and modeling of microwave devices, SM optimization is formulated as a general optimization problem of a surrogate model. This model is a convex combination of a mapped coarse model and a linearized fine model. It exploits, in a

Mohamed H. Bakr; John W. Bandler; Kaj Madsen; José Ernesto Rayas-Sánchez; J. Sondergaard



Application of tabu search to deterministic and stochastic optimization problems  

NASA Astrophysics Data System (ADS)

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 developed. The theoretical underpinnings of the TSMC method and the flow of the algorithm are explained. Its performance is compared to other existing methods for financial option valuation. In the third, and final, problem, TSMC method is used to determine the conditions of feasibility for hybrid electric vehicles and fuel cell vehicles. There are many uncertainties related to the technologies and markets associated with new generation passenger vehicles. These uncertainties are analyzed in order to determine the conditions in which new generation vehicles can compete with established technologies.

Gurtuna, Ozgur


A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks  

PubMed Central

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ?0 minimization problem. Then, we relax this non-convex optimization to a convex ?1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian



The expanded LaGrangian system for constrained optimization problems  

NASA Technical Reports Server (NTRS)

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.



Minimax problems of discrete optimization invariant under majority operators  

NASA Astrophysics Data System (ADS)

A special class of discrete optimization problems that are stated as a minimax modification of the constraint satisfaction problem is studied. The minimax formulation of the problem generalizes the classical problem to realistic situations where the constraints order the elements of the set by the degree of their feasibility, rather than defining a dichotomy between feasible and infeasible subsets. The invariance of this ordering under an operator is defined, and the discrete minimization of functions invariant under majority operators is proved to have polynomial complexity. A particular algorithm for this minimization is described.

Vodolazskii, E. V.; Flach, B.; Schlesinger, M. I.



Social interaction as a heuristic for combinatorial optimization problems  

NASA Astrophysics Data System (ADS)

We investigate the performance of a variant of Axelrod’s model for dissemination of culture—the Adaptive Culture Heuristic (ACH)—on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents’ strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N1/4 so that the number of agents must increase with the fourth power of the problem size, N?F4 , to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F6 which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Fontanari, José F.



A Discrete Lagrangian Algorithm for Optimal Routing Problems  

SciTech Connect

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.

Kosmas, O. T.; Vlachos, D. S.; Simos, T. E. [University of Peloponnese, 22100 Tripoli (Greece)



Application of clustering global optimization to thin film design problems.  


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. PMID:24663856

Lemarchand, Fabien



State-Constrained Optimal Control Problems of Impulsive Differential Equations  

SciTech Connect

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.

Forcadel, Nicolas, E-mail: [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail:; Zidani, Hasnaa, E-mail: [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)



Biogeography-Based Optimization with Blended Migration for Constrained Optimization Problems  

E-print Network

University Cleveland, Ohio ABSTRACT Biogeography-based optimization (BBO) is a new evolutionary algorithm based on the science of biogeography. We propose two extensions to BBO. First, we propose blended migration. Second, we modify BBO to solve constrained optimization problems

Simon, Dan


Artificial bee colony algorithm for solving optimal power flow problem.  


This paper proposes an artificial bee colony (ABC) algorithm for solving optimal power flow (OPF) problem. The objective of the OPF problem is to minimize total cost of thermal units while satisfying the unit and system constraints such as generator capacity limits, power balance, line flow limits, bus voltages limits, and transformer tap settings limits. The ABC algorithm is an optimization method inspired from the foraging behavior of honey bees. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems. The numerical results have indicated that the proposed algorithm can find high quality solution for the problem in a fast manner via the result comparisons with other methods in the literature. Therefore, the proposed ABC algorithm can be a favorable method for solving the OPF problem. PMID:24470790

Le Dinh, Luong; Vo Ngoc, Dieu; Vasant, Pandian



On Optimal AMLI Solvers for Incompressible Navier-Stokes Problems  

NASA Astrophysics Data System (ADS)

We consider the incompressible Navier-Stokes problem and a projection scheme based on Crouzeix-Raviart finite element approximation of the velocities and piece-wise constant approximation of the pressure. These non-conforming finite elements guarantee that the divergence of the velocity field is zero inside each element, i.e., the approximation is locally conservative. We propose optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners for both, the decoupled scalar parabolic problems at the prediction step as well as to the mixed finite element method (FEM) problem at the projection step. The main contribution of the current paper is the obtained scalability of the AMLI methods for the related composite time-stepping solution method. The algorithm for the Navier-Stokes problem has a total computational complexity of optimal order. We present numerical tests for the efficiency of the AMLI solvers for the case of lid-driven cavity flow for different Reynolds numbers.

Boyanova, P.; Margenov, S.



An optimized finite-difference scheme for wave propagation problems  

NASA Technical Reports Server (NTRS)

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.; Lomax, H.; Jurgens, H.



Optimization models for the dynamic facility location and allocation problem  

Microsoft Academic Search

The design of logistic distribution systems is one of the most critical and strategic issues in industrial facility management. The aim of this study is to develop and apply innovative mixed integer programming optimization models to design and manage dynamic (i.e. multi-period) multi-stage and multi-commodity location allocation problems (LAP). LAP belong to the NP-hard complexity class of decision problems, and

Riccardo Manzini; Elisa Gebennini



Advances in dual algorithms and convex approximation methods  

NASA Technical Reports Server (NTRS)

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.

Smaoui, H.; Fleury, C.; Schmit, L. A.



Solution-space structure of (some) optimization problems  

NASA Astrophysics Data System (ADS)

We study numerically the cluster structure of random ensembles of two NP-hard optimization problems originating in computational complexity, the vertex-cover problem and the number partitioning problem. We use branch-and-bound type algorithms to obtain exact solutions of these problems for moderate system sizes. Using two methods, direct neighborhood-based clustering and hierarchical clustering, we investigate the structure of the solution space. The main result is that the correspondence between solution structure and the phase diagrams of the problems is not unique. Namely, for vertex cover we observe a drastic change of the solution space from large single clusters to multiple nested levels of clusters. In contrast, for the number-partitioning problem, the phase space looks always very simple, similar to a random distribution of the lowest-energy configurations. This holds in the ''easy''/solvable phase as well as in the ''hard''/unsolvable phase.

Hartmann, A. K.; Mann, A.; Radenbach, W.



A new filled function algorithm for constrained global optimization problems  

Microsoft Academic Search

A new filled function with one parameter is proposed for solving constrained global optimization problems without the coercive condition, in which the filled function contains neither exponential term nor fractional term and is easy to be calculated. A corresponding filled function algorithm is established based on analysis of the properties of the filled function. At last, we perform numerical experiments

Suxiang He; Weilai Chen; Hui Wang




E-print Network

of singular perturbation problems for Hamilton-Jacobi-Bellman equations motivated by optimal control systems European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN, GA number 264735-SADCO lies in finding out the proper junction condition between 1 and 2 to characterize the value function

Paris-Sud XI, Université de


An augmented Lagrangian optimization method for inflatable structures analysis problems  

Microsoft Academic Search

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton–Raphson scheme was proven to be efficient for solving many nonlinear problems, it can lead to lack of convergence when it is applied to the simulation of the inflation process. As a

M. Bruyneel; P. Jetteur; D. Granville; S. Langlois; C. Fleury



Establishing the optimality of sequencing heuristics for cutting stock problems  

Microsoft Academic Search

Cutting stock problems typically involve the generation of feasible cutting patterns whilst minimizing waste. In some instances the sequence of cutting these patterns is important. One objective of the sequencing stage is to minimize the maximum queue of partially cut orders. This paper presents two exact methods to meet this objective and to determine the optimality of previously introduced sequencing

Boon J. Yuen; Ken V. Richardson



The Air Traffic Flow Management Problem: An Integer Optimization Approach  

E-print Network

The Air Traffic Flow Management Problem: An Integer Optimization Approach Dimitris Bertsimas1 approach can be used as the main engine of managing air traffic in the US. 1 Introduction The continuous. As a result, air traffic flow management (ATFM) has become increasingly cru- cial. ATFM attempts to prevent

Bertsimas, Dimitris


Towards Grid Implementations of Metaheuristics for Hard Combinatorial Optimization Problems  

Microsoft Academic Search

Metaheuristics are approximation algorithms that nd very good solutions to hard combinatorial optimization problems at the expense of large computational require- ments. They do, however, offer a wide range of possibili- ties for implementations of effective robust parallel algo- rithms which run in much smaller computation times. We present four strategies for the parallelization of an extended GRASP with ILS

Cristina Boeres; Vinod E. F. Rebello; Celso C. Ribeiro


Multiagent Optimization System for Solving the Traveling Salesman Problem (TSP)  

Microsoft Academic Search

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),

Xiao-Feng Xie; Jiming Liu



An Asymptotic Method to a Financial Optimization Problem  

E-print Network

Chapter 6 An Asymptotic Method to a Financial Optimization Problem Dejun Xie, David Edwards the mortgage loan balance M.t/ D m c h 1 e ct i ; (6.2) D. Xie ( ), D. Edwards, and G. Schleiniger Department Science+Business Media B.V. 2010 79 #12;80 D. Xie et al. where m denotes the continuous mortgage payment

Edwards, David A.


Solving Globally-Optimal Threading Problems in 'Polynomial-Time'.  

National Technical Information Service (NTIS)

Computational protein 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...

E. C. Uberbacher, D. Xu Y. Xu



To the optimization problem in minority game model  

SciTech Connect

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.

Yanishevsky, Vasyl [Drogobych Ivan Franko University, 36 Ivan Franko St., 82100 (Ukraine)



520 IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 8, NO. 3, JULY 2011 A Convex Optimization Framework for Almost  

E-print Network

Optimization Framework for Almost Budget Balanced Allocation of a Divisible Good Anil Kumar Chorppath efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria

Sundaresan, Rajesh


Optimizing investment fund allocation using vehicle routing problem framework  

NASA Astrophysics Data System (ADS)

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.

Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita



People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours  

PubMed Central

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. PMID:20686597

Acuńa, Daniel E.; Parada, Víctor



Statistical physics of hard combinatorial optimization: Vertex cover problem  

NASA Astrophysics Data System (ADS)

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Zhao, Jin-Hua; Zhou, Hai-Jun



Minimum Convex Partitions and Maximum Empty Polytopes  

E-print Network

Let S be a set of n points in d-space. A convex Steiner partition is a tiling of CH(S) with empty convex bodies. For every integer d, we show that S admits a convex Steiner partition with at most (n-1)/d tiles. This bound is the best possible for affine independent points in the plane, and it is best possible apart from constant factors in every dimension d>= 3. We also give the first constant-factor approximation algorithm for computing a minimum Steiner convex partition of an affine independent point set in the plane. Determining the maximum possible volume of a single tile in a Steiner partition is equivalent to a famous problem of Danzer and Rogers. We give a (1-epsilon)-approximation for the maximum volume of an empty convex body when S lies in the d-dimensional unit box [0,1]^d.

Dumitrescu, Adrian; Tóth, Csaba D



Quantum convex support  

Microsoft Academic Search

Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C?-algebra A, which we call (quantum) convex support. The convex support can be viewed as a projection of the state space of A and it

Stephan Weis



Cores of convex games  

Microsoft Academic Search

The core of ann-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one that is based on a convex set function. In this paper it is shown that the core of a convex game is not empty and that it has an especially regular structure.

Lloyd S. Shapley



Exact multiplicity of positive solutions for concave-convex and convex-concave nonlinearities  

NASA Astrophysics Data System (ADS)

This note gives an unified treatment of the exact multiplicity results for both S-shaped and reversed S-shaped bifurcation for positive solutions of the two-point problem u?+?f(u)=0, for -1convex and convex-concave nonlinearities f(u).

Korman, Philip; Li, Yi



Optimization of Array Controlling for Complex NDT Problems  

NASA Astrophysics Data System (ADS)

The controlling modes of a curved broadband array for pipe inspection and of a plane array for testing of half-finished products are optimized by means of calculating the time harmonic and transient fields. The sound fields are calculated both in water delay and in steel. It is shown that the limitation of the maximum steering angle and the orientation of the single elements are more crucial problems than grating lobes. This publication demonstrates that the controlling can be improved by optimization of the number of elements which operate as an array concurrently and by a variation of the delay times for particular elements.

Kühnicke, Elfgard



Multiresolution strategies for the numerical solution of optimal control problems  

NASA Astrophysics Data System (ADS)

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 nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

Jain, Sachin


A stochastic approach to the problem of spacecraft optimal manoeuvres  

NASA Astrophysics Data System (ADS)

The problem of spacecraft orbit transfer with minimum fuel consumption is considered. A new version of the suboptimal and hybrid control approach of numerically treating the problem, where one can take into account the accuracy in the satisfaction of constraints, is developed. To solve the nonlinear programming problem in each iteration, a stochastic version of the projection of the gradient method is used together with the well known hybrid approach to find the optimal control in this kind of dynamic problem. For the maneuvers considered, the spacecraft is supposed to be in keplerian motion perturbed by the thrustors whenever they are active. These thrustors are assumed to be of fixed magnitude (either low or high) and operating in an on-off mode. The solution is given in terms of the location of the burning arcs, time histories of thrustors attitude (pitch or yaw), final orbit acquired, and fuel consumed. Numerical results are presented.

Dealmeidaprado, Antonio Fernando Bertachin; Neto, Atair Rios



Three Parallel Algorithms for Solving Nonlinear Systems and Optimization Problems  

Microsoft Academic Search

\\u000a In this work we describe three sequential algorithms and their parallel counterparts for solving nonlinear systems, when the\\u000a Jacobian matrix is symmetric and positive definite. This case appears frequently in unconstrained optimization problems. Two\\u000a of the three algorithms are based on Newton’s method. The first solves the inner iteration with Cholesky decomposition while\\u000a the second is based on the inexact

Jesús Peinado; Antonio M. Vidal



New Variants of Genetic Algorithms Applied to Problems of Combinatorial Optimization  

Microsoft Academic Search

Problems of Combinatorial Optimization distinguish themselves by their well-structured problem description as well as by their huge number of possible action alternatives. Especially in the area of production and operational logistics these problems frequently occur. Their advantage lies in their subjective understanding of action alternatives and their objective functions. The use of classical optimization methods for problems of combinatorial optimization

Michael Affenzeller


Random Convex Programs  

E-print Network

a theoretical result (Theorem 6.2) that provides an explicit assessment on “how close” the empirical problem is to the ...... approach to approximate dynamic programming. Mathematics of ... Optimization of risk measures. In G.C. Calafiore and.



An optimization spiking neural p system for approximately solving combinatorial optimization problems.  


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. PMID:24875789

Zhang, Gexiang; Rong, Haina; Neri, Ferrante; Pérez-Jiménez, Mario J



Practical Global Optimization for Multiview Geometry  

Microsoft Academic Search

This paper presents a practical method for finding the provably globally optimal solution to numerous prob- lems in projective geometry including multiview triangula- tion, camera resectioning and homography estimation. Un- like traditional methods which may get trapped in local min- ima due to the non-convex nature of these problems, this ap- proach provides a theoretical guarantee of global optimality. The

Sameer Agarwal; Manmohan Krishna Chandraker; Fredrik Kahl; David J. Kriegman; Serge Belongie



Optimal Parametric Discrete Event Control: Problem and Solution  

SciTech Connect

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 $L$.

Griffin, Christopher H [ORNL



On the degeneracy of the IMRT optimization problem.  


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. PMID:12462725

Alber, M; Meedt, G; Nüsslin, F; Reemtsen, R



Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints  

SciTech Connect

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.

Kmet', Tibor [Department of Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia); Kmet'ova, Maria [Department of Mathematics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia)



On the robust optimization to the uncertain vaccination strategy problem  

NASA Astrophysics Data System (ADS)

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.

Chaerani, D.; Anggriani, N.; Firdaniza



Optimality Conditions for A Two-Stage Reservoir Operation Problem  

NASA Astrophysics Data System (ADS)

This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem within a consistent theoretical framework. The effects of three typical constraints, which are mass balance, non-negative release and storage constraints under both certain and uncertain conditions have been analyzed. When all non-negative constraints and storage constraints are non-binding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over the two stages); while if any of the non-negative release or storage constraints is binding, in general SOP results in the optimal solution except two special cases. One of them is a complement of the traditional SOP/HR curve, which happens while the capacity constraint is binding; the other is a special hedging rule, which should be employed to carry over all water in the current stage to the future, when extreme drought is certain and higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints but in general higher uncertainty level in the future makes HR a more favorable since water needs to be reserved to defense the risk caused by the uncertainty. Using the derived optimality conditions, an algorithm for solving the model numerically has been developed and tested with hypothetical examples.

Zhao, J.; Cai, X.; Wang, Z.



Optimality conditions for a two-stage reservoir operation problem  

NASA Astrophysics Data System (ADS)

This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem using a consistent theoretical framework. The effects of three typical constraints, i.e., mass balance, nonnegative release, and storage constraints under both certain and uncertain conditions are analyzed. When all nonnegative constraints and storage constraints are unbinding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over current and future stages. However, if any of those constraints are binding, SOP results in the optimal solution, except in some special cases which need to carry over water in the current stage to the future stage, when extreme drought is certain and a higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints. A higher uncertainty level in the future makes HR more favorable as water needs to be reserved to defend against the risk caused by uncertainty. Using the derived optimality conditions, an algorithm for solving a numerical model is developed and tested with the Miyun Reservoir in China.

Zhao, Jianshi; Cai, Ximing; Wang, Zhongjing



A mathematical programming approach to stochastic and dynamic optimization problems  

SciTech Connect

We propose three ideas for constructing optimal or near-optimal policies: (1) for systems for which we have an exact characterization of the performance space we outline an adaptive greedy algorithm that gives rise to indexing policies (we illustrate this technique in the context of indexable systems); (2) we use integer programming to construct policies from the underlying descriptions of the performance space (we illustrate this technique in the context of polling systems); (3) we use linear control over polyhedral regions to solve deterministic versions for this class of problems. This approach gives interesting insights for the structure of the optimal policy (we illustrate this idea in the context of multiclass queueing networks). The unifying theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic and dynamic optimization parallels efforts of the mathematical programming community in the last fifteen years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and new algorithms with provable a posteriori guarantees for their suboptimality for polling systems, multiclass queueing and loss networks.

Bertsimas, D.



New attitude penalty functions for spacecraft optimal control problems  

SciTech Connect

A solution of a spacecraft optimal control problem, whose cost function relies on an attitude description, usually depends on the choice of attitude coordinates used. A problem could be solved using 3-2-1 Euler angles or using classical Rodriguez parameters and yield two different ``optimal`` solutions, unless the performance index in invariant with respect to the attitude coordinate choice. Another problem arising with many attitude coordinates is that they have no sense of when a body has tumbled beyond 180{degrees} from the reference attitude. In many such cases it would be easier (i.e. cost less) to let the body complete the revolution than to force it to reverse the rotation and return to the desired attitude. This paper develops a universal attitude penalty function g() whose value is independent of the attitude coordinates chosen to represent it. Furthermore, this function will achieve its maximum value only when a principal rotation of {plus_minus}180{degrees} from the target state is performed. This will implicitly permit the g() function to sense the shortest rotational distance back to the reference state. An attitude penalty function which depends on the Modified Rodriguez Parameters (MRP) will also be presented. These recently discovered MRPs are a non-singular three-parameter set which can describe any three-attitude. This MRP penalty function is simpler than the attitude coordinate independent g() function, but retains the useful property of avoiding lengthy principal rotations of more than {plus_minus}180{degrees}.

Schaub, H.; Junkins, J.L. [Texas A and M Univ., College Station, TX (United States). Dept. of Aerospace Engineering; Robinett, R.D. [Sandia National Labs., Albuquerque, NM (United States)



Mathematical theory of a relaxed design problem in structural optimization  

NASA Technical Reports Server (NTRS)

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.

Kikuchi, Noboru; Suzuki, Katsuyuki



Hybrid Particle Swarm Optimizers in the Single Machine Scheduling Problem: An Experimental Study  

Microsoft Academic Search

Summary. Although Particle Swarm Optimizers (PSO) have been successfully used in a wide variety of continuous optimization problems, their use has not been as widespread in discrete optimization problems, particularly when adopting non-binary encodings. In this chapter, we discuss three PSO variants (which are applied on a specific scheduling problem: the Single Machine Total Weighted Tardiness): a Hybrid PSO (HPSO

Leticia C. Cagnina; Susana C. Esquivel; Carlos A. Coello Coello



Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis  

NASA Astrophysics Data System (ADS)

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.

Izui, K.; Nishiwaki, S.; Yoshimura, M.



Finite element solution of optimal control problems with inequality constraints  

NASA Technical Reports Server (NTRS)

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.

Bless, Robert R.; Hodges, Dewey H.



Algorithms for bilevel optimization  

NASA Technical Reports Server (NTRS)

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.

Alexandrov, Natalia; Dennis, J. E., Jr.



Gerrymandering and Convexity  

ERIC Educational Resources Information Center

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…

Hodge, Jonathan K.; Marshall, Emily; Patterson, Geoff




SciTech Connect

Monte Carlo is quite useful for calculating specific quantities in complex transport problems. Many variance reduction strategies have been developed that accelerate Monte Carlo calculations for specific tallies. However, when trying to calculate multiple tallies or a mesh tally, users have had to accept different levels of relative uncertainty among the tallies or run separate calculations optimized for each individual tally. To address this limitation, an extension of the CADIS (Consistent Adjoint Driven Importance Sampling) method, which is used for difficult source/detector problems, has been developed to optimize several tallies or the cells of a mesh tally simultaneously. The basis for this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. This method utilizes the results of a forward discrete ordinates solution, which may be based on a quick, coarse-mesh calculation, to develop a forward-weighted source for the adjoint calculation. The importance map and the biased source computed from the adjoint flux are then used in the forward Monte Carlo calculation to obtain approximately uniform relative uncertainties for the desired tallies. This extension is called forward-weighted CADIS, or FW-CADIS.

Peplow, Douglas E. [ORNL] [ORNL; Evans, Thomas M [ORNL] [ORNL; Wagner, John C [ORNL] [ORNL



Logical definability and asymptotic growth in optimization and counting problems  

SciTech Connect

There has recently been a great deal of interest in the relationship between logical definability and NP-optimization problems. Let MS{sub n} (resp. MP{sub n}) be the class of problems to compute, for given a finite structure A, the maximum number of tuples {bar x} in A satisfying a {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar x}, {bar S}) as {bar S} ranges over predicates on A. Kolaitis and Thakur showed that the classes MS{sub n} and MP{sub n} collapse to a hierarchy of four levels. Papadimitriou and Yannakakis previously showed that problems in the two lowest levels MS{sub 0} and MS{sub 1} (which they called Max Snp and Max Np) are approximable to within a contrast factor in polynomial time. Similarly, Saluja, Subrahmanyam, and Thakur defined SS{sub n} (resp. SP{sub n}) to be the class of problems to compute, for given a finite structure A, the number of tuples ({bar T}, {bar S}) satisfying a given {Sigma}{sub n} (resp. II{sub n}) formula {psi}({bar T}, {bar c}) in A. They showed that the classes SS{sub n} and SP{sub n} collapse to a hierarchy of five levels and that problems in the two lowest levels SS{sub 0} and SS{sub 1} have a fully polynomial time randomized approximation scheme. We define extended classes MSF{sub n}, MPF{sub n} SSF{sub n}, and SPF{sub n} by allowing formulae to contain predicates definable in a logic known as least fixpoint logic. The resulting hierarchies classes collapse to the same number of levels and problems in the bottom levels can be approximated as before, but now some problems descend from the highest levels in the original hierarchies to the lowest levels in the new hierarchies. We introduce a method characterizing rates of growth of average solution sizes thereby showing a number of important problems do not belong MSF{sub 1} and SSF{sub 1}. This method is related to limit laws for logics and the probabilistic method from combinatorics.

Compton, K. [Univ. of Michigan, Ann Arbor, MI (United States)



Supplier Selection Problems with Considering E-business via Particle Swarm Optimization: Supplier Selection Problems with Considering E-business  

Microsoft Academic Search

In this paper, an optimal mathematical model was constructed to solve the supplier selection problems. The cost factors along with quantity discount policies are considered in the proposed problem. In addition, E-business is taken as an important factor in the supplier appraisal. A Particle Swarm Optimization (PSO) approach is proposed for solving the mathematical model to figure out the suitable

Y. N. Wang; H. S. Wang; Z. H. Che



Human opinion dynamics: An inspiration to solve complex optimization problems  

PubMed Central

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

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan



Human opinion dynamics: an inspiration to solve complex optimization problems.  


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

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P; Kapur, Pawan



Human opinion dynamics: An inspiration to solve complex optimization problems  

NASA Astrophysics Data System (ADS)

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.

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan



Discrete Optimization A filter-and-fan approach to the job shop scheduling problem  

Microsoft Academic Search

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure. Our new search method,

Cesar Rego; Renato Duarte


Chance-Constrained Guidance With Non-Convex Constraints  

NASA Technical Reports Server (NTRS)

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 failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Ono, Masahiro



Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems  

PubMed Central

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka



An optimal quantum algorithm for the oracle identification problem  

E-print Network

In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its dependence on N and M. Our algorithm considerably simplifies and improves the previous best algorithm due to Ambainis et al. Our algorithm also has applications in quantum learning theory, where it improves the complexity of exact learning with membership queries, resolving a conjecture of Hunziker et al. The algorithm is based on ideas from classical learning theory and a new composition theorem for solutions of the filtered $\\gamma_2$-norm semidefinite program, which characterizes quantum query complexity. Our composition theorem is quite general and allows us to compose quantum algorithms with input-dependent query complexities without incurring a logarithmic overhead for error reduction. As an application of the composition theorem, we remove all log factors from the best known quantum algorithm for Boolean matrix multiplication.

Robin Kothari




E-print Network

DECOMPOSITION IN CONIC OPTIMIZATION WITH PARTIALLY SEPARABLE STRUCTURE YIFAN SUN, MARTIN S to extend to conic optimization problems with general non-polyhedral convex cones because the conic patterns. The paper describes a decomposition method that exploits partial separability in conic linear

Vandenberghe, Lieven


Convex Graph Invariants  

E-print Network

The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are ...

Chandrasekaran, Venkat


Stereotype locally convex spaces  

NASA Astrophysics Data System (ADS)

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.

Akbarov, S. S.



Automatic differentiation and spectral projected gradient methods for optimal control problems  

Microsoft Academic Search

Automatic differentiation and nonmonotone spectral projected gradient techniques are used for solving optimal control problems. The original problem is reduced to a nonlinear programming one using general Runge–Kutta integration formulas. Canonical formulas which use a fast automatic differentiation strategy are given to compute derivatives of the objective function. On the basis of this approach, codes for solving optimal control problems

Ernesto G. Birgina; YURI G. EVTUSHENKO



Application of Alternative Multidisciplinary Optimization Formulations to a Model Problem for Static Aeroelasticity  

Microsoft Academic Search

A new model problem for static aeroelasticity is introduced and used to illustrate several alternative approaches for formulating multidisciplinary design optimization problems. The alternatives are distinguished by the kind of analysis problem feasibility that is maintained at each optimization iteration. In the familiar \\

Gregory R. Shubin



Ant colony optimization and local search for bin packing and cutting stock problems  

Microsoft Academic Search

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In

J Levine; F Ducatelle



Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions  

SciTech Connect

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.

Luo Yousong, E-mail: [RMIT University, School of Mathematical and Geospatial Sciences (Australia)



Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems.  


This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations. PMID:17550112

Wang, Yong; Cai, Zixing; Guo, Guanqi; Zhou, Yuren



An iterative row-action method for interval convex programming  

Microsoft Academic Search

The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form minf(x), subject

Y. Censor; A. Lent



Advancement and analysis of Gauss pseudospectral transcription for optimal control problems  

E-print Network

As optimal control problems become increasingly complex, innovative numerical methods are needed to solve them. Direct transcription methods, and in particular, methods involving orthogonal collocation have become quite ...

Huntington, Geoffrey Todd, 1979-



Finite element approximation of an optimal control problem for the von Karman equations  

NASA Technical Reports Server (NTRS)

This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

Hou, L. Steven; Turner, James C.



Optimal experimental design applied to DC resistivity problems  

E-print Network

The systematic design of experiments to optimally query physical systems through manipulation of the data acquisition strategy is termed optimal experimental design (OED). This dissertation introduces the state-of-the-art ...

Coles, Darrell Ardon, 1971-



A One Dimensional Deterministic Free Boundary Problem  

Microsoft Academic Search

A general one dimensional deterministic inflnite horizon singular optimal control problem with unbounded control set is considered in this paper. Using the dynamic programming approach we prove that the value function is convex, and C1 along the free boundary. Also, we

Frontera Libre; Guillermo Ferreyra; Jesus A. Pascal



An Exact Algorithm for Optimal Areal Positioning Problem with Rectangular Targets and Requests  

E-print Network

In this thesis, we introduce a new class of problems, which we call Optimal Areal Positioning (OAP), and study a special form of these problems. OAPs have important applications in earth observation satellite management, tele-robotics, multi...

Bansal, Manish



Polynomial implementations of Newton`s method for a class of combinatorial optimization problems  

SciTech Connect

We use Newton type schemes to produce polynomial algorithms for a class of combinatorial optimization problems. As a special case, we produce an alternate polynomial scheme for the weighted 1-centre problem in the plane.

Kabadi, S. [Univ. of New Brunswick, NJ (United States); Aneja, Y.



Decomposition of the convex simplex method  

Microsoft Academic Search

Rutenberg (Ref. 1) provided a decomposition method to solve the problem of minimizing a separable, nonlinear objective function with large-scale linear constraints by using the convex simplex method (Ref. 2). However, there seem to be some errors in his paper (Ref. 3). This paper will rebuild the method by using more convenient and consistent notation.

W. S. Hsia



Duality Results for Conic Convex Programming  

Microsoft Academic Search

This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone in finite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include Gordon-Stiemke

Zhi-quan Luo; Jos F. Sturm; Shuzhong Zhang



A hybrid optimization algorithm for the job-shop scheduling problem  

Microsoft Academic Search

The job-shop scheduling problem is a NP-hard combinational optimization and one of the best-known machine scheduling problems. Genetic algorithm is an effective search algorithm to solve this problem; however the quality of the best solution obtained by the algorithm has to improve due to its limitation. The paper proposes a novel hybrid optimization algorithm for the job-shop scheduling problem, which

Qiang Zhou; Xunxue Cui; Zhengshan Wang; Bin Yang



Structure preserving integrators for solving linear quadratic optimal control problems with applications to describe the flight of a quadrotor  

E-print Network

Structure preserving integrators for solving linear quadratic optimal control problems Valencia, Spain. Abstract We present structure preserving integrators for solving linear quadratic optimal control problems. This problem requires the numerical integration of matrix Riccati differential equations

Blanes, Sergio


Robustness in Combinatorial Optimization and Scheduling Theory ...  

E-print Network

new and quickly developing area of combinatorial optimization. It deals .... A generalized interior point algorithm for convex objective functions has been .... Averbakh I. The minmax regret permutation flow shop problem with two jobs. ..... The robust tabu search firstly introduced in this paper is a new and original technique.



Particle Swarm Optimization for the Steiner Tree in Graph and Delay-Constrained Multicast Routing Problems  

E-print Network

investigation on applying a Particle Swarm Optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many and Steiner tree problems from the OR library. The experimental results show the superior performance

Qu, Rong


An Improved Ant Colony Optimization for Flexible Job Shop Scheduling Problems  

Microsoft Academic Search

An improved ant colony optimization (IACO) algorithm is proposed to the flexible job shop scheduling problem (FJSSP) in this paper. IACO algorithm provides an effective integration between ant colony optimization (ACO) model and knowledge model. In the IACO algorithm, knowledge model learns some available knowledge from the optimization of ACO, and then employs the existing knowledge to guide the current

Dong-sheng Xu; Xiao-yan Ai; Li-ning Xing



A Knowledge-Based Ant Colony Optimization for Flexible Job Shop Scheduling Problems  

Microsoft Academic Search

A Knowledge-Based Ant Colony Optimization (KBACO) algorithm is proposed in this paper for the Flexible Job Shop Scheduling Problem (FJSSP). KBACO algorithm provides an effective integration between Ant Colony Optimization (ACO) model and knowledge model. In the KBACO algorithm, knowledge model learns some available knowledge from the optimization of ACO, and then applies the existing knowledge to guide the current

Li-Ning Xing; Ying-Wu Chen; Peng Wang; Qing-Song Zhao; Jian Xiong



A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems  

E-print Network

1 A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems Nasser R. Sabar1 of the Honey-bee Mating Optimization Algorithm for solv- ing educational timetabling problems. The honey-bee algorithm is a nature inspired algorithm which sim- ulates the process of real honey-bees mating

Qu, Rong


Mixed integer programming based nested partition algorithm for facility location optimization problems  

Microsoft Academic Search

Facility location optimization is very important for many retail industries, such as banking network, chain stores, and so on. Maximal covering location problem (MCLP) is one of the well-known models for these facility location optimization problems, which has earned extensive research interests. However, various practical requirements limit the application of the traditional formulation of MCLP, and the NP-hard characteristic makes

Li Xia; Yanjia Zhao; Ming Xie; Jinyan Shao; Jin Dong



Solving Continuous-Time Optimal-Control Problems with a Spreadsheet.  

ERIC Educational Resources Information Center

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)

Naevdal, Eric



Varying fitness functions in genetic algorithm constrained optimization: the cutting stock and unit commitment problems  

Microsoft Academic Search

We present a specific varying fitness function technique in genetic algorithm (GA) constrained optimization. This technique incorporates the problem's constraints into the fitness function in a dynamic way. It consists of forming a fitness function with varying penalty terms. The resulting varying fitness function facilitates the GA search. The performance of the technique is tested on two optimization problems: the

Vassilios Petridis; Spiridon A. Kazarlis; Anastasios Bakirtzis



A sequential approximation method using neural networks for engineering design optimization problems  

Microsoft Academic Search

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often ‘pass–fail’, ‘0–1’ type binary constraints. This paper presents a sequential approximation method specifically for engineering optimization problems with

Yeh-Liang Hsu; Shu-Gen Wang; Chia-Chieh Yu



Application of Particle Swarm Optimization for Traveling Salesman Problem to lossless compression of color palette images  

Microsoft Academic Search

This paper investigates optimal color indexing for the compression of color palette images. This work enhances the recent traveling salesman problem (TSP) based re-indexing technique with particle swarm optimization (PSO). In this work, color re-indexing is done by solving the problem as a TSP using PSO. The proposed technique, yields better compression gains than the recent work that used a

Joshua Van Hook; Ferat Sahin; Ziya Arnavut



A Particle Swarm Optimization and Differential Evolution Algorithms for Job Shop Scheduling Problem  

Microsoft Academic Search

In this paper, we present particle swarm optimization (PSO) and differential evolution (DE) algorithms for the job shop scheduling problem with the makespan criterion. The applications of PSO and DE on combinatorial optimization problems are still considered limited, but the advantages of PSO and DE algorithms such as structural simplicity, accessibility to practical applications, ease of implementatio n, speed to

M. Fatih Tasgetiren; Mehmet Sevkli; Yun-Chia Liang; M. Mutlu Yenisey



Motivation Basic models Optimization model A real world problem Outlook Tactical Ambulance Location and Relocation  

E-print Network

Motivation Basic models Optimization model A real world problem Outlook Tactical Ambulance Location / 28 #12;Motivation Basic models Optimization model A real world problem Outlook Outline 1. Motivation) Tactical Ambulance Location and Relocation November 22, 2013 2 / 28 #12;Motivation Basic models

Al Hanbali, Ahmad


The Automatic Formulating Method of the Optimal Operating Planning Problem for Energy Supply Systems  

Microsoft Academic Search

The problem of the optimal operating planning for energy supply system is formulated as mixed-integer linear programming (MILP), but, it is too complicated for most untrained operators with little experience to apply the method. This paper proposes an automatic evaluating method of the optimal operating planning for energy supply system in using simple data. The problem can be formulated only

Naohiko Suzuki; Takaharu Ueda; Koichi Sasakawa



A Geometric Analysis of Bang-Bang Extremals in Optimal Control Problems for Combination Cancer Chemotherapy*  

E-print Network

Chemotherapy* Heinz Sch¨attler Dept. of Electrical and Systems Engineering, Washington University, St. Louis of cancer cells under combination chemotherapies are considered as multi-input optimal control problems over for chemotherapy over a fixed therapy interval. For these problems, and consistent with medical practice, optimal

Ledzewicz, Urszula


20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev  

E-print Network

20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev ABSTRACT. The appearance of optimization problems in the field of air pollution modeling and their importance arising in air pollution modeling will be considered. We shall present a review of some approaches

Dimov, Ivan


Convex Quantum Logic  

E-print Network

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. This differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement.

F. Holik; C. Massri; N. Ciancaglini



Carbon footprint optimization: game theoretic problems and solutions  

Microsoft Academic Search

We discuss four problems that we have identified under the umbrella of carbon economics problems: carbon credit allocation (CCA), carbon credit buying (CCB), carbon credit selling (CCS), and carbon credit exchange (CCE). Because of the strategic nature of the players involved in these problems, game theory and mechanism design provides a natural way of formulating and solving these problems. We

Deepak Bagchi; Shantanu Biswas; Y. Narahari; P. Suresh; L. Udaya Lakshmi; N. Viswanadham; S. V. Subrahmanya


Lift-and-Project Cuts for Mixed Integer Convex Programs  

Microsoft Academic Search

\\u000a This paper addresses the problem of generating cuts for mixed integer nonlinear programs where the objective is linear and\\u000a the relations between the decision variables are described by convex functions defining a convex feasible region. We propose\\u000a a new method for strengthening the continuous relaxations of such problems using cutting planes. Our method can be seen as\\u000a a practical implementation

Pierre Bonami


Flow Control as Stochastic Optimal Control Problem with Incomplete Information  

E-print Network

in TCP/IP networks. In particular, the optimal control demonstrates a much smoother behavior than the currently used TCP/IP congestion control. Index Terms--- TCP/IP, Stochastic Processes, Stochastic Optimal Control. I. INTRODUCTION T HE transmission of most Internet data flows is governed by TCP (Transmission

Avrachenkov, Konstantin


Hybrid genetic algorithm research and its application in problem optimization  

Microsoft Academic Search

There is a lot of research in genetic algorithm about structural optimization. But as far as the large multi-goal program is concerned, it limits the application of genetic algorithm for the reason of its specialty and large calculation. In order to explore a new resolution, the author proposed a combining algorithm for structural optimization, which is based on genetic algorithm

Weijin Jiang I; Dingti Luol; Yusheng Xu; Xingming Sun



An approach to the multi-axis problem in manual control. [optimal pilot model  

NASA Technical Reports Server (NTRS)

The multiaxis control problem is addressed within the context of the optimal pilot model. The problem is developed to provide efficient adaptation of the optimal pilot model to complex aircraft systems and real world, multiaxis tasks. This is accomplished by establishing separability of the longitudinal and lateral control problems subject to the constraints of multiaxis attention and control allocation. Control solution adaptation to the constrained single axis attention allocations is provided by an optimal control frequency response algorithm. An algorithm is developed to solve the multiaxis control problem. The algorithm is then applied to an attitude hold task for a bare airframe fighter aircraft case with interesting multiaxis properties.

Harrington, W. W.



[Design method of convex master gratings for replicating flat-field concave gratings].  


Flat-field concave diffraction grating is the key device of a portable grating spectrometer with the advantage of integrating dispersion, focusing and flat-field in a single device. It directly determines the quality of a spectrometer. The most important two performances determining the quality of the spectrometer are spectral image quality and diffraction efficiency. The diffraction efficiency of a grating depends mainly on its groove shape. But it has long been a problem to get a uniform predetermined groove shape across the whole concave grating area, because the incident angle of the ion beam is restricted by the curvature of the concave substrate, and this severely limits the diffraction efficiency and restricts the application of concave gratings. The authors present a two-step method for designing convex gratings, which are made holographically with two exposure point sources placed behind a plano-convex transparent glass substrate, to solve this problem. The convex gratings are intended to be used as the master gratings for making aberration-corrected flat-field concave gratings. To achieve high spectral image quality for the replicated concave gratings, the refraction effect at the planar back surface and the extra optical path lengths through the substrate thickness experienced by the two divergent recording beams are considered during optimization. This two-step method combines the optical-path-length function method and the ZEMAX software to complete the optimization with a high success rate and high efficiency. In the first step, the optical-path-length function method is used without considering the refraction effect to get an approximate optimization result. In the second step, the approximate result of the first step is used as the initial value for ZEMAX to complete the optimization including the refraction effect. An example of design problem was considered. The simulation results of ZEMAX proved that the spectral image quality of a replicated concave grating is comparable with that of a directly recorded concave grating. PMID:19839358

Zhou, Qian; Li, Li-Feng



Multi-population Binary ant Colony Algorithm with Concrete Behaviors for multi-objective optimization problem  

Microsoft Academic Search

Aiming at solving the drawbacks of the original binary ant colony algorithm on multi-objective optimization problems: easy to fall into the local optimization and difficult to get the Pareto optimal solutions, we proposed Multi-population Binary ant Colony Algorithm with Concrete Behaviors (MPBACB). The algorithm introduced multi-population method to ensure the globe optimization ability, and use environmental evaluation\\/reward model to improve

Ye Qing; Xiong Wei-Qing; Jiang Bao-chuan



Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation  

Microsoft Academic Search

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms\\u000a of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation,\\u000a where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic\\u000a algorithm and an LM-BFGS algorithm in order

B. Ivorra; A. M. Ramos; B. Mohammadi



A permutation-based dual genetic algorithm for dynamic optimization problems  

Microsoft Academic Search

Adaptation to dynamic optimization problems is currently receiving growing interest as one of the most important applications\\u000a of genetic algorithms. Inspired by dualism and dominance in nature, genetic algorithms with the dualism mechanism have been\\u000a applied for several dynamic problems with binary encoding. This paper investigates the idea of dualism for combinatorial optimization\\u000a problems in dynamic environments, which are also

Lili Liu; Dingwei Wang; W. H. Ip



Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation  

NASA Technical Reports Server (NTRS)

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.

Mook, D. J.; Lew, Jiann-Shiun



Optimization Online - Stochastic p-Robust Location Problems  

E-print Network

Aug 3, 2004 ... In this paper, we present facility location models that combine the two ... on two classical facility location problems, the P-median problem and the ... Citation: Technical Report #04T-014, July 2004, Department of Industrial and ...

Lawrence V. Snyder



Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes.  


The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks. PMID:24295962

Müller, Stefan; Regensburger, Georg; Steuer, Ralf



Problem Formulations for Simulation-based Design Optimization ...  

E-print Network

Feb 17, 2014 ... a tree implements a partition of the design space X. Each interior node implements ...... imentations may allow to build a decision process to chose the most ... Genetic Algorithms in Search, Optimization and Machine Learning.

B. Talgorn, S. Le Digabel, M. Kokkolaras



Cut Generation for Optimization Problems with Multivariate Risk ...  

E-print Network

Aug 14, 2014 ... ... range of views and involve differing opinions of multiple experts (for motivating ...... Then, by simple manipulation and linearizing the terms [z ? c xi]+ =: vi using .... this operation does not change the set of optimal solutions.



Solving Two-stage Robust Optimization Problems by A Constraint ...  

E-print Network

looks for solutions that are immune from any perturbation within a predefined ... portfolio optimization [15] and power system control and scheduling [18, 12, 9]. ..... can only be installed in a site with a facility built and the supply cannot exceed



Discrete bat algorithm for optimal problem of permutation flow shop scheduling.  


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. PMID:25243220

Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang



Hyperspectral image superresolution: An edge-preserving convex formulation  

E-print Network

Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of images with high spatial and spectral resolutions from HSI-MSI pairs. In this paper, we formulate this data fusion problem as the minimization of a convex objective function containing two data-fitting terms and an edge-preserving regularizer. The data-fitting terms are quadratic and account for blur, different spatial resolutions, and additive noise; the regularizer, a form of vector Total Variation, promotes aligned discontinuities across the reconstructed hyperspectral bands. The optimization described above is rather hard, owing to its non-diagonalizable linear operators, to the non-quadratic and non-smooth nature of the regularizer, and to the very large size of the image to be inferred. We tac...

Simőes, Miguel; Almeida, Luis B; Chanussot, Jocelyn



Computational and statistical tradeoffs via convex relaxation  

PubMed Central

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

Chandrasekaran, Venkat; Jordan, Michael I.



Reducing computation time in DFP (Davidon, Fletcher & Powell) update method for solving unconstrained optimization problems  

NASA Astrophysics Data System (ADS)

Solving the unconstrained optimization problems is not easy and DFP update method is one of the methods that we can work with to solve the problems. In unconstrained optimization, the time computing needed by the method's algorithm to solve the problems is very vital and because of that, we proposed a hybrid search direction for DFP update method in order to reduce the computation time needed for solving unconstrained optimization problems. Some convergence analysis and numerical results of the hybrid search direction were analyzed and the results showed that the proposed hybrid search direction strictly reduce the computation time needed by DFP update method and at the same time increase the method's efficiency which is sometimes fail for some complicated unconstrained optimization problems.

Sofi, A. Z. M.; Mamat, M.; Ibrahim, M. A. H.



New evolutionary genetic algorithms for NP-complete combinatorial optimization problems  

Microsoft Academic Search

Evolutionary genetic algorithms have been proposed to solve NP-complete combinatorial optimization problems. A new crossover operator based on group theory has been created. Computational processes motivated by proposed evolutionary genetic algorithms were described as stochastic processes, using population dynamics and interactive markovian chains. The proposed algorithms were used in solving flowshop problems and an asymmetric traveling salesman problem. The experimental

Fam Quang Bac; V. L. Perov



A Global Optimization Approach to a Water Distribution Network Design Problem  

Microsoft Academic Search

In this paper, we address a global optimization approach to a waterdistribution network design problem. Traditionally, a variety of localoptimization schemes have been developed for such problems, each new methoddiscovering improved solutions for some standard test problems, with noknown lower bound to test the quality of the solutions obtained. A notableexception is a recent paper by Eiger et al. (1994)

Hanif D. Sherali; Ernest P. Smith



A comparison of optimization-based approaches for solving the aerodynamic design problem  

NASA Technical Reports Server (NTRS)

Three optimization-based methods for solving aerodynamic design problems are compared. The Euler equations for one-dimensional duct flow was used as a model problem, and the three methods are compared for efficiency, robustness, and implementation difficulty. The smoothness of the design problem with respect to different shock-capturing finite difference schemes, and in the presence of grid refinement, is investigated.

Frank, Paul D.; Shubin, Gregory R.



Discrete Optimization Solving the semi-desirable facility location problem using  

E-print Network

Discrete Optimization Solving the semi-desirable facility location problem using bi-obnoxious facility location problem is introduced. The new model is com- posed of a weighted minisum function The semi-obnoxious facility location problem [5­8,17,30,37,41] has drawn much recent attention among

Smith, Alice E.


Computing Large Sparse Multivariate Optimization Problems with an Application in Biophysics  

E-print Network

Computing Large Sparse Multivariate Optimization Problems with an Application in Biophysics for the analysis of a biophysics problem, which is representative for a large class of problems in the physical, chosen from the field of biophysics, is analytical ultracentrifugation (AUC) [1, 2, 3]. AUC is a powerful

Boppana, Rajendra V.


An Ant Colony Optimization Approach for the MultiLevel Unconstrained Lot-Sizing Problem  

Microsoft Academic Search

An ant colony optimization approach for the multilevel unconstrained lot-sizing problem (MLULSP) is described and evaluated using 176 benchmark problems from the literature, with problem sizes varying from 5 to 500 products and up to 52 periods. The approach consists of a binary encoding of production plans. The lot-sizing decisions are mapped on a routing graph to apply the metaheuristic

Jörg Homberger; Hermann Gehring



Generalising submodularity and horn clauses: Tractable optimization problems defined by tournament pair multimorphisms  

Microsoft Academic Search

The submodular function minimization problem (SFM) is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial-time algorithms have recently been discovered to solve this problem. The most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally-ordered finite set and whose range includes both finite and

David A. Cohen; Martin C. Cooper; Peter G. Jeavons



A steady-state solution for the optimal pavement resurfacing problem  

Microsoft Academic Search

This paper presents a solution approach for the problem of optimising the frequency and intensity of pavement resurfacing, under steady-state conditions. If the pavement deterioration and improvement models are deterministic and follow the Markov property, it is possible to develop a simple but exact solution method. This method removes the need to solve the problem as an optimal control problem,

Yuwei Li; Samer Madanat



Discrete-time entropy formulation of optimal and adaptive control problems  

NASA Technical Reports Server (NTRS)

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.

Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.



Two stages optimization problem: New variant of Bin Packing Problem for decision making  

Microsoft Academic Search

In this paper, we present a new multi-criteria assignment problem that groups characteristics from the well known Bin Packing Problem (BPP) and Generalized Assign- ment Problem (GAP). Similarities and differences between these problems are discussed, and a new variant of BPP is presented. The new variant will be called generalized assignment problem with identified first-use bins (GAPIFB). The GAPIFB will

Ahmad H. Shraideh; Hervé G. Camus; Pascal G. M. Yim



The effect of model uncertainty on some optimal routing problems  

NASA Technical Reports Server (NTRS)

The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included.

Mohanty, Bibhu; Cassandras, Christos G.



Initial parameters problem of WNN based on particle swarm optimization  

NASA Astrophysics Data System (ADS)

The stock price prediction by the wavelet neural network is about minimizing RMSE by adjusting the parameters of initial values of network, training data percentage, and the threshold value in order to predict the fluctuation of stock price in two weeks. The objective of this dissertation is to reduce the number of parameters to be adjusted for achieving the minimization of RMSE. There are three kinds of parameters of initial value of network: w , t , and d . The optimization of these three parameters will be conducted by the Particle Swarm Optimization method, and comparison will be made with the performance of original program, proving that RMSE can be even less than the one before the optimization. It has also been shown in this dissertation that there is no need for adjusting training data percentage and threshold value for 68% of the stocks when the training data percentage is set at 10% and the threshold value is set at 0.01.

Yang, Chi-I.; Wang, Kaicheng; Chang, Kueifang



Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints  

NASA Astrophysics Data System (ADS)

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.

Lim, Byung Hwa; Shin, Yong Hyun; Choi, U. Jin



Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations  

E-print Network

This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general ...

Mittal, Shashi, Ph. D. Massachusetts Institute of Technology



Topological classification of closed convex sets in Frechet spaces  

E-print Network

We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowoslki and Torunczyk, this result implies that each closed convex subset of a Frechet space is homemorphic to $[0,1]^n\\times [0,1)^m\\times l_2(k)$ for some cardinals $0\\le n\\le\\omega$, $0\\le m\\le 1$ and $k\\ge 0$.

Banakh, Taras



Finite dimensional approximation of a class of constrained nonlinear optimal control problems  

NASA Technical Reports Server (NTRS)

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.

Gunzburger, Max D.; Hou, L. S.



On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems  

Microsoft Academic Search

Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density $f$ of a random variable $X$ based on $n$ i.i.d. observations from $Y = X + \\\\varepsilon$, where $\\\\varepsilon$ is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights

Jianqing Fan



Nonlinear switched capacitor `neural' networks for optimization problems  

Microsoft Academic Search

A systematic approach is presented for the design of analog neural nonlinear programming solvers using switched-capacitor (SC) integrated circuit techniques. The method is based on formulating a dynamic gradient system whose state evolves in time toward the solution point of the corresponding programming problem. A neuron cell for the linear and the quadratic problem suitable for monolithic implementation is introduced.

A. Rodriguez-Vazquez; R. Dominguez-Castro; A. Rueda; J. L. Huertas; E. Sanchez-Sinencio



Models and Algorithms for Some Combinatorial Optimization Problems: University Course Timetabling, Facility Layout and Integrated Production-Distribution Scheduling.  

E-print Network

??In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems… (more)

Wang, Yuqiang



Some Marginalist Intuition Concerning the Optimal Commodity Tax Problem  

ERIC Educational Resources Information Center

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,…

Brett, Craig



Optimal Control Problems for Mathematical Models of Cancer  

E-print Network

Illinois University Edwardsville, Il, USA NetCO 2014 Conference on New Trends in Optimal Control, Tours, France July 23-27, 2014 Heinz Sch�ttler Washington University St. Louis, Mo, USA hal-01024610,version1-17Jul2014 #12;Collaborators and Support Helmut Maurer Rheinisch Westf�lische Wilhelms-Universit�t M

Boyer, Edmond


Oppositional Biogeography-Based Optimization for Combinatorial Problems  

E-print Network

(BBO). Simulations on TSP benchmarks illustrate that incorporating opposition into BBO improves its. Biogeography-based optimization (BBO) [3], [4] is an evolutionary algorithm, derived from the study of biogeography. BBO is inspired by the migration of species amongst islands and imitates this pattern to solve

Simon, Dan


Inverse boundary value problems with unknown boundaries: Optimal stability  

NASA Astrophysics Data System (ADS)

In this paper we obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining, accessible, part of the boundary. We treat the case of arbitrary space dimension n?2 . Such problems arise in applied contexts of nondestructive testing of materials for either electric or thermal conductors, and are known to be ill-posed.

Alessandrini, Giovanni; Beretta, Elena; Rosset, Edi; Vessella, Sergio


Integer Partitions and Convexity  

NASA Astrophysics Data System (ADS)

Let n be an integer >=1, and let p(n,k) and P(n,k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdos.

Bouroubi, Sadek



Convex bodies of states and maps  

NASA Astrophysics Data System (ADS)

We give a general solution to the question of when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density operators. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.

Grabowski, Janusz; Ibort, Alberto; Ku?, Marek; Marmo, Giuseppe



Quasi-convex reproducing kernel meshfree method  

NASA Astrophysics Data System (ADS)

A quasi-convex reproducing kernel approximation is presented for Galerkin meshfree analysis. In the proposed meshfree scheme, the monomial reproducing conditions are relaxed to maximizing the positivity of the meshfree shape functions and the resulting shape functions are referred as the quasi-convex reproducing kernel shape functions. These quasi-convex meshfree shape functions are still established within the framework of the classical reproducing or consistency conditions, namely the shape functions have similar form as that of the conventional reproducing kernel shape functions. Thus this approach can be conveniently implemented in the standard reproducing kernel meshfree formulation without an overmuch increase of computational effort. Meanwhile, the present formulation enables a straightforward construction of arbitrary higher order shape functions. It is shown that the proposed method yields nearly positive shape functions in the interior problem domain, while in the boundary region the negative effect of the shape functions are also reduced compared with the original meshfree shape functions. Subsequently a Galerkin meshfree analysis is carried out by employing the proposed quasi-convex reproducing kernel shape functions. Numerical results reveal that the proposed method has more favorable accuracy than the conventional reproducing kernel meshfree method, especially for structural vibration analysis.

Wang, Dongdong; Chen, Pengjie



A Lagrangean heuristic for the facility location problem with staircase costs  

Microsoft Academic Search

In this paper we develop and compare heuristic solution methods for the capacitated facility location problem with staircase shaped production cost functions, a linear mixed integer programming problem with a large proportion of integer variables. We propose a Lagrangean heuristic, including Lagrangean relaxation and subgradient optimization as a base for an efficient primal heuristic, and using convex piecewise linearizations of

Kaj Holmberg; Jonas Ling



Optimal Control Study of Interception Problems Prof. Hugh H.T. Liu  

E-print Network

literature review and report the state-of-the-art of the problem; · to pick one approach (with supervisor. The student will choose one optimal control approach as a test case, to provide in-depth study with computer

Liu, Hugh H.T.


Particle Swarm Inspired Evolutionary Algorithm (PS-EA) for Multiobjective Optimization Problems  

E-print Network

-3], Evolutionary Strategies (ES) [4], Evolutionary Programming (EP) [5] and Artificial Immune Systems (AIS) [6 by the paradigm of birds flocking. PSO is successfully implemented in various optimization problems like weight

Coello, Carlos A. Coello


Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer  

NASA Technical Reports Server (NTRS)

The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.

Miele, A.; Basapur, V. K.



The Optimizing-Simulator: An Illustration Using the Military Airlift Problem  

E-print Network

and Phrases: Approximate dynamic programming, military logistics, control of simulation, modeling information14 The Optimizing-Simulator: An Illustration Using the Military Airlift Problem TONGQIANG TONY WU and logistics: simulation, offering tremendous modeling flexibility, and op- timization, which offers

Powell, Warren B.


Optimal Stopping under Probability Distortion  

E-print Network

We formulate an optimal stopping problem where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. In particular, we show that the optimality of the exit time of an interval (corresponding to the "cut-loss-or-stop-gain" strategy widely adopted in stock trading) is endogenous for problems with convex distortion functions, including ones where distortion is absent. We also discuss economical interpretations of the results.

Xu, Zuo Quan



Optimal location of a service facility as a problem in basic mechanics  

NASA Astrophysics Data System (ADS)

The economic problem of locating optimally a service facility in a two-dimensional Euclidean space is equivalent to a problem of equilibrium between forces in statics. A mechanical analog, suggested at the beginning of the century, as well as more modern numerical methods for the solution of the problem, are discussed. The multifacility problem, which is an extension to the original one, is also mentioned. Cases in which the cost involved is nonlinearly dependent on the Euclidean distance are briefly referred to.

Chen, Reuven



On the Complexity of the Traveling Umpire Problem - Optimization ...  

E-print Network

The traveling umpire problem (TUP) consists of determining which games will be handled by each one of ... The TUP was created as an abstraction of the real-life umpire ...... tation (ISAAC), volume 5878 of Lecture Notes in Computer Science, ...



Solving Infinite-dimensional Optimization Problems by Polynomial ...  

E-print Network

subspaces of the original infinite-dimensional space and solve the corresponding ... a continuous time setting lead to infinite-dimensional problems. † The first author is a ... In this work, we consider a different method of resolution that does not ...



Two-Stage Robust Power Grid Optimization Problem  

E-print Network

transmission capacity limits for a given planning horizon (e.g., one week) ... gramming approaches to solve the problem with the objective of minimizing the total expected cost. ... which has a significant share of combined heat and power units.



Solving the schedule transition problem using optimization techniques  

E-print Network

A new algorithm is introduced for effectively solving the airline schedule transition problem, which involves efficiently re-routing aircraft in order to balance the number and the types of aircraft at each station at the ...

Fujiwara, Tsuneo



39 Most Tensor Problems are NP-Hard - Optimization Online  

E-print Network

tractability of their problems in light of modern complexity theory. ...... on Computational Advances in Multi-Sensor Adaptive Process. (CAMSAP), 1 (2005) .... M.A.O. Vasilescu, “Human motion signatures: analysis, synthesis, recognition,” Proc.



A linked simulation–optimization model for solving the unknown groundwater pollution source identification problems  

Microsoft Academic Search

This study proposes a linked simulation–optimization model for solving the unknown groundwater pollution source identification problems. In the proposed model, MODFLOW and MT3DMS packages are used to simulate the flow and transport processes in the groundwater system. These models are then integrated with an optimization model which is based on the heuristic harmony search (HS) algorithm. In the proposed simulation–optimization

M. Tamer Ayvaz



Hybridization of genetic algorithm with immune system for optimization problems in structural engineering  

Microsoft Academic Search

Optimization is the task of getting the best solution among the feasible solutions. There are many methods available to obtain\\u000a an optimized solution. Genetic algorithm (GA), which is a heuristic type of optimization method, is discussed in this paper.\\u000a The focus of the paper is the use of GA for large dimensionality design problems, where computational efficiency is a major

S. Rajasekaran; S. Lavanya



Optimal allocation and control problems for software-testing resources  

Microsoft Academic Search

Two kinds of software-testing management problems are considered: testing-resource allocation to best use specified testing resources during module testing, and a testing-resource control problem concerning how to spend the allocated amount of testing-resource expenditures during it. A software reliability growth model based on a nonhomogeneous Poisson process is introduced. The model describes the time-dependent behavior of software errors detected and

Hiroshi Ohtera; Shigeru Yamada



The optimization of job shop scheduling problem based on Artificial Fish Swarm Algorithm with tabu search strategy  

Microsoft Academic Search

The job shop scheduling problem (JSSP) is a sort of famous combination optimization problems which is difficult to solve using the conventional optimization algorithm. Artificial Fish Swarm Algorithm (AFSA) proves to be powerful in solving some optimization problems and the AFSA has the advantages of not strict to parameter setting, strong robustness, fast convergence and so on. In this paper,

Kongcun Zhu; Mingyan Jiang



Motion Planning with Sequential Convex Optimization and Convex Collision Checking  

E-print Network

considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We for delivering radiation to OB/GYN tumors [Garg et al., 2013]. plays two important roles in robot motion planning

North Carolina at Chapel Hill, University of


A combined strategy for optimization in nonlinear magnetic problems using simulated annealing and search techniques  

Microsoft Academic Search

A combined strategy for optimization of electromagnetic devices based on a two-stage scheme is described. Two different ways of implementing a simulated annealing algorithm, one for discrete and one for continuous variables, have been implemented and tested. The second one proved to be more reliable and problem-independent than the other. This technique was used in a combined optimization strategy in

G. Drago; A. Manella; M. Nervi; M. Repetto; G. Secondo



Comparison among evolutionary algorithms and classical optimization methods for circuit design problems  

Microsoft Academic Search

This work concerns the comparison of evolu- tionary algorithms and standard optimization methods on two circuit design problems: the parameter extrac- tion of device circuit model and the multi-objective op- timization of an Operational Transconductance Ampli- fier. We compare standard optimization techniques and evolutionary algorithms in terms of quality of the solu- tions and computational effort, that is, objective func-

Angelo Marcello Anile; Vincenzo Cutello; Giuseppe Nicosia; Rosario Rascunŕ; Salvatore Spinella



A new hybrid optimization algorithm for the job-shop scheduling problem  

Microsoft Academic Search

A new hybrid optimization algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling environment. The new algorithm is based on the principle of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs

Xia Weijun; Wu Zhiming; Zhang Wei; Yang Genke



The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots  

E-print Network

The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots of Minnesota Minneapolis, MN 55455 Email: {hjmin|npapas} Abstract-- This work presents a novel multi-robot coverage scheme for an unknown number of robots; it focuses on optimizing the number of robots and each

Minnesota, University of


Anti-predatory particle swarm optimization: Solution to nonconvex economic dispatch problems  

Microsoft Academic Search

This paper proposes a new particle swarm optimization (PSO) strategy namely, anti-predatory particle swarm optimization (APSO) to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle (bird) is governed by three behaviors: inertial, cognitive and social. The cognitive and social behaviors are the components of the foraging activity, which help the swarm of birds to

A. Immanuel Selvakumar; K. Thanushkodi



A Novel Approach to Dynamic Optimization of ODE and DAE Systems as High-Index Problems  

Microsoft Academic Search

Solution of many problems in plant operations requires determination of optimal control profi les subject to state constraints for systems modeled by ordinary differential equations (ODEs) or dif ferential-alge- braic equations (DAEs). For example, optimal temperature and\\/or feed rate profiles are important for the oper - ation of many batch reactions. Similar observations apply to reflux policies for batch distillation,

William F. Feehery; Julio R. Banga; Paul I. Barton


Blessings of maintaining infeasible solutions for constrained multi-objective optimization problems  

Microsoft Academic Search

The most common approach to handling constraints in a constrained optimization problem has been the use of penalty functions. In recent years non-dominance based ranking methods have been applied for an efficient handling of constraints. These techniques favor the feasible solutions over the infeasible solutions, thus guiding the search through the feasible space. Usually the optimal solutions of the constrained

Amitay Isaacs; Tapabrata Ray; Warren Smith



An Improved Particle Swarm Optimization-Based Approach for Production Scheduling Problems  

Microsoft Academic Search

Job-shop scheduling problem (JSSP) is very common in a discrete manufacturing environment. It deals with multi-operation models, which are different from the flow shop models. It is usually very hard to find its optimal solution. In this paper, a new hybrid approach in dealing with this job-shop scheduling problem based on particle swarm optimization (PSO) and simulated annealing (SA) technique

Fuqing Zhao; Qiuyu Zhang; Yahong Yang



A dual method for optimal control problems with initial and final boundary constraints.  

NASA Technical Reports Server (NTRS)

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.

Pironneau, O.; Polak, E.



Reduction of dimension of optimal estimation problems for dynamical systems with singular perturbations  

NASA Astrophysics Data System (ADS)

The possibility of applying the method of integral manifolds to the reduction of optimal filtering problems for systems with low energy dissipation is explored. For such systems, it is shown that the slow subsystem of matrix Riccati differential equations turns out to have a higher dimension than expected, which leads to an increase in the dimension of the reduced problems. An optimal filter is constructed for the Langevin equation and for a dynamic model of a single-link flexible manipulator.

Osintsev, M. S.; Sobolev, V. A.



Motzkin decomposition of closed convex sets  

Microsoft Academic Search

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. This paper provides five characterizations of the larger class of closed convex sets in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve

M. A. Goberna; E. González; J. E. Martínez-Legaz; M. I. Todorov



Analysis and formulation of a class of complex dynamic optimization problems  

NASA Astrophysics Data System (ADS)

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 simultaneous approach to a wider class of problems, a PDE-constrained optimal control problem, the spatial discretization of which results in a DAE-constrained problem with an arbitrarily high-index inequality constraint, is studied. Optimal control problems with high-index path constraints are very hard to solve, numerically. Contrary to the intuitive belief that the direct transcription approach would not work for the high-index optimal control problem, an analysis is performed to show that NLP-based methods have flexibility with respect to constraint qualifications, and this can be put to use in the context of high-index inequality path-constrained problems to obtain meaningful solutions. (Abstract shortened by UMI.)

Kameswaran, Shivakumar


NIPS workshop: Discrete Optimization in Machine Learning: Connecting Theory and Practice (Lake Tahoe, December 9, 2013)  

E-print Network

Tahoe, December 9, 2013) Discrete Convex Analysis: Basics, DC Programming, and Submodular Welfare Algorithm Kazuo Murota (U. Tokyo) 131209NIPSlakeTahoe 1 #12;Discrete Convex Analysis Convexity Paradigm in Discrete Optimization Matroid Theory + Convex Analysis Submodular fn Matroid base L-convex fn M

Murota, Kazuo


Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods.  


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

Terekhov, Alexander V; Zatsiorsky, Vladimir M



Optimization of a Flow Shop System of Initially Controllable Machines  

Microsoft Academic Search

We consider an optimization problem for deterministic flow shop systems of traditional machines with service costs penalizing small service times. A regular completion-time cost is also included so as to complete jobs as early as possible. The service times are assumed to be initially controllable, i.e., they are set at the startup time. Assuming convexity of the cost functions, we

Kagan Gokbayrak; Omer Selvi



On the Optimality of Generalized (S,S) Policies.  

National Technical Information Service (NTIS)

A standard inventory model is examined with a concave increasing ordering cost function rather than simply a linear one with a setup cost. A generalized (s,S) policy is shown to be optimal in the n-period problem. A generalization of K-convex and quasi-co...

E. L. Porteus




E-print Network

of the MAGLEV train, a new bullet train under development in Japan, is formulated as the continuous convex words. second-order cone programming, interior-point methods, magnetic shielding, MAGLEV train, optimal as similar problems with different linear equality constraints [15]. The bullet train, which is called MAGLEV

Tsuchiya, Takashi


Generating optimal Sturmian basis functions for atomic problems  

SciTech Connect

In this paper we discuss the optimization of Sturmian basis functions by studying bound atomic systems within the configuration interaction method. Our investigation clearly shows how the fulfillment of correct physical boundary conditions at short and large distances from the nucleus improves the convergence rate of the method. This is illustrated first through a one-electron atom, and then with the two-electron systems. For the ground state of the helium atom, and with 35 Sturmian functions per electron and angular momenta, we obtain an energy of -2.903 712 820 a.u., outperforming previous similar calculations [Bromley and Mitroy, Int. J. Quantum Chem. 107, 1150 (2007)].

Randazzo, J. M.; Frapiccini, A. L.; Colavecchia, F. D. [Centro Atomico Bariloche and CONICET, 8400 Bariloche, Rio Negro (Argentina); Ancarani, L. U. [Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine-Metz France, F-57078 Metz (France); Gasaneo, G. [Departamento de Fisica, Universidad Nacional del Sur and CONICET, 8000 Bahia Blanca, Buenos Aires (Argentina)



Computing Optimal Islands C. Bautista  

E-print Network

Computing Optimal Islands C. Bautista J.M. D´iaz-B´a~nez D. Lara§ P. P´erez-Lantero ¶ J. Urrutia I S is called an island of S, if I2 is the intersection of S and a convex set C. An island of S is monochromatic a monochromatic4 island of maximum cardinality. The previous best running time for this problem was O(n3 log n)5

Díaz-Báñez, José Miguel


An Optimal Adaptive Finite Element Method for the Stokes Problem  

Microsoft Academic Search

A new adaptive nite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. For a sequence of nite element spaces with respect to adaptively rened partitions, in the outmost loop the solution is approximated by that of the Stokes problem in which the

Yaroslav Kondratyuk; Rob Stevenson



Quantum Measurements for Hidden Subgroup Problems with Optimal Sample Complexity  

E-print Network

One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for the sample complexity of the identification and decision versions of the hidden subgroup problem. As a consequence of the bounds, we show that the sample complexity for both of the decision and identification versions is $\\Theta(\\log|\\HH|/\\log p)$ for a candidate set $\\HH$ of hidden subgroups in the case that the candidate subgroups have the same prime order $p$, which implies that the decision version is at least as hard as the identification version in this case. In particular, it does so for the important instances such as the dihedral and the symmetric hidden subgroup problems. Moreover, the upper bound of the identification is attained by the pretty good measurement. This shows that the pretty good measurement can identify any hidden subgroup of an arbitrary group with at most $O(\\log|\\HH|)$ samples.

Masahito Hayashi; Akinori Kawachi; Hirotada Kobayashi



Particle swarm optimization for various types of economic dispatch problems  

Microsoft Academic Search

This paper describes a successful adaptation of the particle swarm optimisation (PSO) algorithm to solve various types of economic dispatch (ED) problems in power systems such as, multi-area ED with tie line limits, ED with multiple fuel options, combined environmental economic dispatch, and the ED of generators with prohibited operating zones. Numerical examples typical to each type are solved on

D. N. Jeyakumar; T. Jayabarathi; T. Raghunathan



A New Method for Mapping Optimization Problems onto Neural Networks  

E-print Network

. This approach maps the problems onto Potts glass rather than spin glass theories. A systematic prescription field theory equations, makes it possible to consistently avoid chaotic bahaviour. When exploring 2 #12; 1 Motivation and Results Neural Networks have shown great promise

Peterson, Carsten


New numerical methods for open-loop and feedback solutions to dynamic optimization problems  

NASA Astrophysics Data System (ADS)

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 is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

Ghosh, Pradipto


Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem  

PubMed Central

The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs. PMID:23983808

Jiang, Mingfeng; Jiang, Shanshan; Zhu, Lingyan; Wang, Yaming; Huang, Wenqing; Zhang, Heng



Space Exploration and Global Optimization for Computationally Intensive Design Problems: A Rough Set Based Approach  

E-print Network Abstract Modern engineering design problems often involve computation-intensive analysis and simulation methods, such as the Computer Steering and Visual Steering methods, strive to enable engineers to interact1 Space Exploration and Global Optimization for Computationally Intensive Design Problems: A Rough

Wang, Gaofeng Gary


An improved Particle Swarm Optimization algorithm and its application to a class of JSP problem  

Microsoft Academic Search

In this paper, we analyze the special job shop scheduling problem (JSP) of actual production system in large-scale structure workshops. With regard to this kind of JSP problem, two novel mathematical models (deterministic model and stochastic model) are proposed. In addition, particle swarm optimization (PSO) algorithm is used in the paper because of its high efficiency, and binary PSO algorithm

Kun Fan; Ren-qian Zhang; Guoping Xia



Shadow prices and well-posedness in the problem of optimal investment and consumption with  

E-print Network

Shadow prices and well-posedness in the problem of optimal investment and consumption;Outline Objective Statement of the problem Literature Shadow prices Our shadow price approach Solution the so called "shadow price" approach treat all possible values of parameters (and therefore, study

Sîrbu, Mihai


Optimizing the Slab Yard Planning and Crane Scheduling Problem using a Two-Stage Approach  

E-print Network

Optimizing the Slab Yard Planning and Crane Scheduling Problem using a Two-Stage Approach Anders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Slab Yard Planning and Container Stacking . . . . . . . . 6 2.3.2 Crane Scheduling Modeling - The Crane Scheduling Problem 19 5.1 Precedence Relations


On convexity of H-infinity Riccati solutions and its applications  

NASA Technical Reports Server (NTRS)

The celebrated two-Riccati-equation solution to a standard H-infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H-infinity controllers if the optimal H-infinity norm or gamma, an upper bound of a suboptimal H-infinity norm, is given. In this note, some properties of these H-infinity Riccati solutions are revealed. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H-infinity norm.

Li, X. P.; Chang, B. C.



Lagrangian support vector regression via unconstrained convex minimization.  


In this paper, a simple reformulation of the Lagrangian dual of the 2-norm support vector regression (SVR) is proposed as an unconstrained minimization problem. This formulation has the advantage that its objective function is strongly convex and further having only m variables, where m is the number of input data points. The proposed unconstrained Lagrangian SVR (ULSVR) is solvable by computing the zeros of its gradient. However, since its objective function contains the non-smooth 'plus' function, two approaches are followed to solve the proposed optimization problem: (i) by introducing a smooth approximation, generate a slightly modified unconstrained minimization problem and solve it; (ii) solve the problem directly by applying generalized derivative. Computational results obtained on a number of synthetic and real-world benchmark datasets showing similar generalization performance with much faster learning speed in accordance with the conventional SVR and training time very close to least squares SVR clearly indicate the superiority of ULSVR solved by smooth and generalized derivative approaches. PMID:24374970

Balasundaram, S; Gupta, Deepak; Kapil



Finite element solution of optimal control problems with state-control inequality constraints  

NASA Technical Reports Server (NTRS)

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.

Bless, Robert R.; Hodges, Dewey H.



Convexity, Classification, and Risk Bounds  

Microsoft Academic Search

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0-1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of

Peter L. Bartlett; Michael I. Jordan; Jon D. McAuliffe



Optimizing Constrained Single Period Problem under Random Fuzzy Demand  

NASA Astrophysics Data System (ADS)

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.

Taleizadeh, Ata Allah; Shavandi, Hassan; Riazi, Afshin



The Sizing and Optimization Language, (SOL): Computer language for design problems  

NASA Technical Reports Server (NTRS)

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.

Lucas, Stephen H.; Scotti, Stephen J.



Linear-convex singular control in two dimensions  

Microsoft Academic Search

A two-dimensional linear-convex deterministic singular control problem is posed and solved. The interest here is the explicitness of the results and the relation between the geometry of the drift along the free boundary of the problem and the principle of smooth fit

Guillermo Ferreyra; Omar Hijab



Duality and Self-Duality for Conic Convex Programming  

Microsoft Academic Search

This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone.In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular, we introduce the notions of weak\\/strong feasibility or infeasibility for a general

Z. Q. Luo; Jos F. Sturm; S. Zhang



Relationship Between MP and DPP for the Stochastic Optimal Control Problem of Jump Diffusions  

SciTech Connect

This paper is concerned with the stochastic optimal control problem of jump diffusions. The relationship between stochastic maximum principle and dynamic programming principle is discussed. Without involving any derivatives of the value function, relations among the adjoint processes, the generalized Hamiltonian and the value function are investigated by employing the notions of semijets evoked in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether a given admissible control is optimal.

Shi Jingtao, E-mail:; Wu, Zhen, E-mail: [Shandong University, School of Mathematics (China)



Optimization of the facility location-allocation problem in a customer-driven supply chain  

Microsoft Academic Search

This paper develops and applies an integrated multiple criteria decision making approach to optimize the facility location-allocation\\u000a problem in the contemporary customer-driven supply chain. Unlike the traditional optimization techniques, the proposed approach,\\u000a combining the analytic hierarchy process (AHP) and the goal programming (GP) model, considers both quantitative and qualitative\\u000a factors, and also aims at maximizing the benefits of deliverer and

William Ho; Carman Ka Man Lee; George To Sum Ho



Solution of a Sub-Riemannian Optimal Control Problem for a Quantum Spin System  

Microsoft Academic Search

Experiments in nuclear magnetic resonance (NMR) spectroscopy and NMR quantum computing require control of ensembles of quantum mechanical systems. The controlled transfer of coherence along a one-dimensional chain of spin systems plays a key role in NMR spectroscopy of proteins, and spin chains have also been proposed for NMR quantum information processing. The problem of time-optimal or energy-optimal control of

Amit K. Sanyal; Christopher Moseley; Anthony Bloch


Stochastic Learning via Optimizing the Variational Inequalities.  


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. PMID:25291732

Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei



Selecting radiotherapy dose distributions by means of constrained optimization problems.  


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 instrumental in deriving good quality tests to select radiotherapy treatment plans in rather general situations. PMID:24599739

Alfonso, J C L; Buttazzo, G; García-Archilla, B; Herrero, M A; Núńez, L



Solution of the optimal plant location and sizing problem using simulated annealing and genetic algorithms  

SciTech Connect

In the optimal plant location and sizing problem it is desired to optimize cost function involving plant sizes, locations, and production schedules in the face of supply-demand and plant capacity constraints. We will use simulated annealing (SA) and a genetic algorithm (GA) to solve this problem. We will compare these techniques with respect to computational expenses, constraint handling capabilities, and the quality of the solution obtained in general. Simulated Annealing is a combinatorial stochastic optimization technique which has been shown to be effective in obtaining fast suboptimal solutions for computationally, hard problems. The technique is especially attractive since solutions are obtained in polynomial time for problems where an exhaustive search for the global optimum would require exponential time. We propose a synergy between the cluster analysis technique, popular in classical stochastic global optimization, and the GA to accomplish global optimization. This synergy minimizes redundant searches around local optima and enhances the capable it of the GA to explore new areas in the search space.

Rao, R.; Buescher, K.L.; Hanagandi, V.



Solving optimization problem of space factor of multiple CPV trackers using "butterfly approach"  

NASA Astrophysics Data System (ADS)

Optimization of land use to multi-tracker CPV system is discussed by mathematical approach. Optimization problem using butterfly plot (Contour plot on the shading to adjacent tracker) is discussed to seek optimum allocation pattern. With initial solutions given by this optimum allocation pattern, numerical optimization calculation is done to obtain the optimum allocation including, skew angle to the North-South axis, aspect ratio between X and Y pitch and optimum panel aspect ratio. It is suggested that there are two candidate of optimum allocation pattern.

Araki, Kenji



The economic lot scheduling problem under power-of-two policy  

Microsoft Academic Search

We present further analysis on the economic lot scheduling problem (ELSP) without capacity constraints under power-of-two (PoT) policy. We explore its optimality structure and discover that the optimal objective value is piece-wise convex. By making use of the junction points of this function, we derive an effective (polynomial-time) search algorithm to secure a global optimal solution. The conclusions of this

S. E. Elmaghraby



Energy Minimization for Real-Time Systems with Non-Convex and Discrete Operation Modes  

E-print Network

Energy Minimization for Real-Time Systems with Non-Convex and Discrete Operation Modes Foad Dabiri of California Los Angeles email: {dabiri, alireza, miodrag, majid} @ Abstract--We present an optimal

Potkonjak, Miodrag


The Convex Coordinates of the Symmedian Point  

ERIC Educational Resources Information Center

In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…

Boyd, J. N.; Raychowdhury, P. N.



Using a modified invasive weed optimization algorithm for a personalized urban multi-criteria path optimization problem  

NASA Astrophysics Data System (ADS)

The personalized urban multi-criteria quasi-optimum path problem (PUMQPP) is a branch of multi-criteria shortest path problems (MSPPs) and it is classified as a NP-hard problem. To solve the PUMQPP, by considering dependent criteria in route selection, there is a need for approaches that achieve the best compromise of possible solutions/routes. Recently, invasive weed optimization (IWO) algorithm is introduced and used as a novel algorithm to solve many continuous optimization problems. In this study, the modified algorithm of IWO was designed, implemented, evaluated, and compared with the genetic algorithm (GA) to solve the PUMQPP in a directed urban transportation network. In comparison with the GA, the results have shown the significant superiority of the proposed modified IWO algorithm in exploring a discrete search-space of the urban transportation network. In this regard, the proposed modified IWO algorithm has reached better results in fitness function, quality metric and running-time values in comparison with those of the GA.

Pahlavani, Parham; Delavar, Mahmoud R.; Frank, Andrew U.



A review of recent evolutionary computation-based techniques in wind turbines layout optimization problems  

Microsoft Academic Search

This paper presents a mini-review of the main works recently published about optimal wind turbines layout in wind farms. Specifically,\\u000a we focus on discussing articles where evolutionary computation techniques have been applied, since this computational framework\\u000a has obtained very good results in different formulations of the problem. A summary of the main concepts needed to face the\\u000a problem are also

S. Salcedo-Sanz; B. Saavedra-Moreno; A. Paniagua-Tineo; L. Prieto; A. Portilla-Figueras



Optimizing Constrained Mixed-Integer Nonlinear Programming Problems Using Nature Selection  

Microsoft Academic Search

Many practical engineering optimization problems involving real and integer\\/discrete design variables have been drawing much more attention from researchers. In this paper, an effective adaptive real-parameter simulated annealing genetic algorithm (ARSAGA) was proposed, applied to cope with constrained mixed-integer nonlinear programming problems. The performances of this proposed algorithm, including reliability and convergence speed are demonstrated by examples. It is noted

Rong-Song He



Study of hybrid methods for approximating the Edgeworth-Pareto hull in nonlinear multicriteria optimization problems  

NASA Astrophysics Data System (ADS)

Methods for approximating the Edgeworth-Pareto hull (EPH) of the set of feasible criteria vectors in nonlinear multicriteria optimization problems are examined. The relative efficiency of two EPH approximation methods based on classical methods of searching for local extrema of convolutions of criteria is experimentally studied for a large-scale applied problem (with several hundred variables). A hybrid EPH approximation method combining classical and genetic approximation methods is considered.

Berezkin, V. E.; Lotov, A. V.; Lotova, E. A.



An ant colony optimization algorithm for the redundancy allocation problem (RAP)  

Microsoft Academic Search

This paper uses an ant colony meta-heuristic optimization method to solve the redundancy allocation problem (RAP). The RAP is a well known NP-hard problem which has been the subject of much prior work, generally in a restricted form where each subsystem must consist of identical components in parallel to make computations tractable. Meta-heuristic methods overcome this limitation, and offer a

Yun-chia Liang; Alice E. Smith



Hybridizing tabu search with ant colony optimization for solving job shop scheduling problems  

Microsoft Academic Search

The manufacturing industry continues to be a prime contributor and it requires an efficient schedule. Scheduling is the allocation\\u000a of resources to activities over time and it is considered to be a major task done to improve shop-floor productivity. Job\\u000a shop problem comes under this category and is combinatorial in nature. Research on optimization of the job shop problem is

V. P. Eswaramurthy; A. Tamilarasi



An intelligent genetic algorithm designed for global optimization of multi-minima functions  

Microsoft Academic Search

Many practical problems often lead to large non-convex non-linear programming problems that have multi-minima. The global optimization algorithms of these problems have received much attention over the last few years. Generally, stochastic algorithms are suitable for these problems, but not efficient when there are too many minima. Genetic algorithms are stochastic search approaches based on randomized operators, such as selection,

Li-ning Xing; Ying-wu Chen; Huai-ping Cai



Final Report of Optimization Algorithms for Hierarchical Problems, with Applications to Nanoporous Materials  

SciTech Connect

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 solving discretized optimization models. Our optimization models are multi-level models, however. They are more general, involving different governing equations at each level. A major aspect of this project was the development of flexible software that can be used to solve a variety of hierarchical optimization problems.

Nash, Stephen G.



Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint.  


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. PMID:24991645

Bacanin, Nebojsa; Tuba, Milan



Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint  

PubMed Central

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. PMID:24991645



VeriQuickhull: fast sequential and parallel algorithms for computing the planar convex hull  

E-print Network

Computing the convex hull of a set of points in the plane is one of the most studied problems in computational geometry. The Quickhull algorithm is a popular convex hull algorithm. While the main structure of Quickhull is axed, many different...

Sambasivam, Mashilamani



A Linear time algorithm for computing the Voronoi diagram of a convex polygon  

Microsoft Academic Search

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n points in the plane can be computed in &THgr;(n) time when these points form the vertices of a convex polygon in, say, counterclockwise order. This settles an outstanding open problem in computational geometry. Our

Alok Aggarwal; Leonidas J. Guibas; James B. Saxe; Peter W. Shor



A Linear-Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon  

Microsoft Academic Search

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram ofn sites in the plane can be computed in ?(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order. This settles an open problem in computational geometry. Our techniques can

Alok Aggarwal; Leonidas J. Guibas; James B. Saxe; Peter W. Shor



Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions  

Microsoft Academic Search

Environmental problems are becoming more and more important for our world and their importance will even increase in the future. High pollution of air, water and soil may cause damage to plants, animals and humans. Therefore, the development of industry must be coupled with the protection of the environment, especially in fast-growing countries like Vietnam. In this talk we deal

Matthias Ehrhardt


Transformation techniques for minimax optimal control problems and their application to optimal flight trajectories in a windshear - Optimal abort landing trajectories  

NASA Technical Reports Server (NTRS)

The optimal-control problem of abort-landing trajectories in the presence of low-altitude wind shear is investigated analytically. The vertical-plane Newtonian motion of a point-mass aircraft in a steady wind field is modeled, and a sequential gradient-restoration algorithm is applied. Numerical results showing the effects of wind-shear intensity, initial altitude, and power-setting rate are presented in extensive graphs and discussed in detail. Optimal trajectories for strong or severe wind shears are found to begin with a descent, followed by level flight and then an ascent after leaving the shear region.

Miele, A.; Wang, T.; Melvin, W. W.; Tzeng, C. Y.



Superresolution of passive millimeter-wave images using a combined maximum-likelihood optimization and projection-onto-convex-sets approach  

NASA Astrophysics Data System (ADS)

Imagery data acquired from Passive Millimeter-Wave (PMMW) radiometers have inherently poor resolution due to limited aperture dimensions and the consequent diffraction limits thus requiring processing by a sophisticated super- resolution algorithm before the images can be used for nay useful purposes such as surveillance, fusion, navigation and missile guidance. Recent research has produced a class of powerful algorithms that employ a Bayesian framework in order to iteratively optimize a likelihood function in the resolution enhancement process. These schemes, popularly called ML algorithms, enjoy several advantages such as simple digital implementation and robustness of performance to inaccurate estimation of sensor parameters. However, the convergence of iterations could in some cases become rather slow and practical implementations may require executing a large number of iterations before desired resolution levels can be achieved. The quality of restoration and the extent of achievable super-resolution depend on the accuracy and the amount of a prior information that could be utilized in processing the input imagery dat. Projection-based set- theoretic methods offer a considerable flexibility in incorporating available a priori information and hence provide an attractive framework for tailoring powerful restoration and super-resolution algorithms. The prior information, which is used as constraints during the processing, can be derived form a number of sources such as the phenomenology of the sensor employed, known conditions at the time of recording data, and scene-related information that could be extracted from the image. In this paper, we shall describe a POCS approach to image restoration and use it to enhance the super-resolution performance of ML algorithms. A new algorithm, termed POCS-assisted ML algorithm, that combines the strong points of ML and POCS approaches will be outlined. A quantitative evaluation of the performance of this algorithm for restoring and super- resolving PMMW image data will also be presented.

Sundareshan, Malur K.; Bhattacharjee, Supratik



Ball Versus Distance Convexity of Metric Spaces  

Microsoft Academic Search

We consider two dierent notions of convexity of metric spaces, namely (strict\\/uniform) ball convexity and (strict\\/uniform) distance convexity. Our main theorem states that (strict\\/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict\\/uniform) ball convexity, not even when considering the Euclidean product. MSC 2000:

Thomas Foertsch



Tracking and Optimal Control Problems in Human Head/Eye Coordination  

E-print Network

Tracking and Optimal Control Problems in Human Head/Eye Coordination Indika Wijayasinghe1, Eugenio Aulisa1, Bijoy K. Ghosh1, Stefan Glasauer2,3 and Olympia Kremmyda4 Abstract-- Human head and eye rotate and compares simulation results with experimentally measured data on human head/eye movement. Index Terms

Ghosh, Bijoy K.


Least-squares finite element methods for optimization and control problems for  

E-print Network

, structural mechanics, etc., are very similar. More recently, mathematicians, scientists, and engineers haveLeast-squares finite element methods for optimization and control problems for the Stokes equations why naively defined penalty meth- ods may not be practical. Then, practical penalty methods

Bochev, Pavel



E-print Network

OPTIMALITY OF T-COERCIVITY FOR SCALAR INTERFACE PROBLEMS BETWEEN DIELECTRICS AND METAMATERIALS Anne are real-valued negative parameters when dissipa- tion is neglected. They are usually called metamaterials and a metamaterial, set in an open, bounded subset of Rd , with d = 2, 3. Our aim is to characterize occurences where


A Modified PRP Conjugate Gradient Algorithm with Trust Region for Optimization Problems  

Microsoft Academic Search

In this article, a modified PRP algorithm is presented for unconstrained optimization problems. This method possesses sufficiently descent property and the proposed direction is in a trust region. The global convergence and the linear convergence rate of the given method are established under weaker conditions. Numerical results show that the presented method is effective.

Xiangrong Li; Qingsong Ruan



Bifurcation of Singular Arcs in an Optimal Control Problem for Cancer Immune System Interactions under Treatment  

E-print Network

, 63130-4899, Abstract-- A mathematical model for cancer treatment that includesBifurcation of Singular Arcs in an Optimal Control Problem for Cancer Immune System Interactions under Treatment Urszula Ledzewicz Dept. of Mathematics and Statistics, Southern Illinois University

Ledzewicz, Urszula


Strategic Planning in Air Traffic Control as a Multi-objective Stochastic Optimization Problem  

E-print Network

to solve an artificial benchmark problem involving 24 aircraft and 11 sectors, and is able to provide importantly as far as security is concerned, requested avoidance of an hazardous weather phenomenon area, any important textbook in optimal control, as [1], or artificial intelligence, as [2] and [3

Paris-Sud XI, Université de


Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems  

E-print Network

Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control, 2007 Abstract In this paper, we consider numerous inventory control problems for which the base-stock base-stock levels. The existing stochastic approximation methods in the literature guarantee

Topaloglu, Huseyin


A Hybrid Method of Genetic Algorithms and Ant Colony Optimization to Solve the Traveling Salesman Problem  

Microsoft Academic Search

A new hybrid method iterative extended changing crossover operators which can efficiently obtain the optimum solution of the traveling salesman problem through flexibly alternating ant colony optimization (ACO) which simulates process of learning swarm intelligence in ants' feeding behavior and edge assembly crossover (EAX) which has been recently noticed as an available method for efficient selection of optimum solution with

Ryouei Takahashi



An interval branch and bound algorithm for bound constrained optimization problems  

Microsoft Academic Search

In this paper, we propose modifications to a prototypical branch and bound algorithm for nonlinear optimization so that the algorithm efficiently handles constrained problems with constant bound constraints. The modifications involve treating subregions of the boundary identically to interior regions during the branch and bound process, but using reduced gradients for the interval Newton method. The modifications also involve preconditioners

R. Baker Kearfott



A branch and bound algorithm for bound constrained optimization problems without derivatives  

Microsoft Academic Search

In this paper, we give a new branch and bound algorithm for the global optimization problem with bound constraints. The algorithm is based on the use of inclusion functions. The bounds calculated for the global minimum value are proved to be correct, all rounding errors are rigorously estimated. Our scheme attempts to exclude most “uninteresting” parts of the search domain

Christian Jansson; Olaf Knüppel



Discrete Optimization A heuristic for the multi-period petrol station replenishment problem  

Microsoft Academic Search

In the multi-period petrol station replenishment problem (MPSRP) the aim is to optimize the delivery of several petro- leum products to a set of petrol stations over a given planning horizon. One must determine, for each day of the planning horizon, how much of each product should be delivered to each station, how to load these products into vehicle compart-

Fabien Cornillier; Fayez F. Boctor; Gilbert Laporte; Jacques Renaud



E-print Network

, in many practical suspension bridges the total weight of the bridge, instead of being uniformly on a suspended cable of extraneous applied forces such as arising from the live loads on a practical suspension bridge. However, in the real world, the problem of finding an optimal construction shape is more

Vanderbei, Robert J.


A Global Optimization Method for the Molecular Replacement Problem in X-ray Crystallography  

E-print Network

of Computational and Applied Mathematics, Rice University, Houston, Texas, USA. 1 #12; X-ray crystallography hasA Global Optimization Method for the Molecular Replacement Problem in X-ray Crystallography #3 The primary technique for determining the three-dimensional structure of a protein molecule is X-ray

Zhang, Yin


On the statistical mechanics of optimization problems of the travelling salesman type  

E-print Network

L-1145 On the statistical mechanics of optimization problems of the travelling salesman type J in an acceptable time. For several years, S. Kirkpatrick has advocated the use of statistical mechanics tools » in a way that closely follows the introduction of the canonical ensemble in statistical mechanics

Paris-Sud XI, Université de


A Trajectory Method for the Optimization of the Multi-Facility Location Problem With lp Distances  

Microsoft Academic Search

We consider the multi-facility location problem of placing m new facilities optimally among n demand points (or existing facilities) so that the sum of all weighted lp distance pairs (facility to facility and facility to demand point) is minimized. A method involving the solution of differential equations by numerical integration is presented. This method is computationally comparable to many existing

Z. Drezner; G. O. Wesolowsky



Optimal solutions for the machining economics problem with stochastically distributed tool lives  

Microsoft Academic Search

This paper proposes analytical models and numerical procedures for simultaneously determining the optimal cutting speed and tool replacement policy in machining economics problems with stochastic tool lives when the objective is the minimization of the machining cost per part. It is shown that the objective function is separable for certain phase type tool life distributions, including Gamma, which leads to

Eleftherios Iakovou; Chi M. Ip; Christos Koulamas



A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems  

Microsoft Academic Search

This paper proposes a new version of the classical particle swarm optimization (PSO), namely, new PSO (NPSO), to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle is governed by three behaviors, namely, inertial, cognitive, and social. The cognitive behavior helps the particle to remember its previously visited best position. This paper proposes a split-up

A. Immanuel Selvakumar; K. Thanushkodi



Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches  

Microsoft Academic Search

The objective of the Economic Dispatch Problems (EDPs) of electric power generation is to schedule the committed generating units outputs so as to meet the required load demand at minimum operating cost while satisfying all units and system equality and inequality constraints. Recently, global optimization approaches inspired by swarm intelligence and evolutionary computation approaches have proven to be a potential

Leandro dos Santos Coelho; Chu-Sheng Lee



Greedy algorithms Algorithms for solving (optimization) problems typically go through a  

E-print Network

Greedy algorithms Algorithms for solving (optimization) problems typically go through a sequence of steps, with a set of choices at each step. A greedy algorithm always makes the choice that looks best at the moment, without regard for future consequence "take what you can get now" strategy Greedy algorithms do

Bai, Zhaojun


A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem  

Microsoft Academic Search

. From a computational point of view, the job-shop schedulingproblem is one of the most notoriously intractable NP-hard optimizationproblems. In spite of a great deal of substantive research, thereare instances of even quite modest size for which it is beyond our currentunderstanding to solve to optimality. We propose several new lowerbounding procedures for this problem, and show how to incorporate

Paul Martin; David B. Shmoys



Bee Colony Optimization algorithm with Big Valley landscape exploitation for Job Shop Scheduling problems  

Microsoft Academic Search

Scheduling is a crucial activity in semiconductor manufac- turing industry. Effective scheduling in its operations leads to improvement in the efficiency and utilization of its equipment. Job Shop Scheduling is an NP-hard problem which is closely related to some of the scheduling activities in this industry. This paper presents an improved Bee Col- ony Optimization algorithm with Big Valley landscape

Li-pei Wong; Chi Yung Puan; Malcolm Yoke-hean Low; Chin Soon Chong



Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems  

Microsoft Academic Search

The prime contributor to the development of the competitive market is the manufacturing industry which requires a good schedule. Scheduling is the allocation of resources to activities over time. Scheduling is considered to be a major task done to improve the shop-floor productivity. The job shop problem is under this category and is combinatorial in nature. Research on optimization of

V. P. Eswaramurthy; A. Tamilarasi


Generating Hard Test Instances with Known Optimal Solution for the Rectilinear Quadratic Assignment Problem  

Microsoft Academic Search

In this paper we consider the rectilinear version of the quadratic assignment problem (QAP). We define a class of edge-weighted graphs with nonnegatively valued bisections. For one important type of such graphs we provide a characterization of point sets on the plane for which the optimal value of the related QAP is zero. These graphs are used in the algorithms

G. Palubeckis




E-print Network

INVARIANTS FOR HOMOLOGY CLASSES WITH APPLICATION TO OPTIMAL SEARCH AND PLANNING PROBLEM IN ROBOTICS are of frequent occurrence as configuration spaces of robots, where O represent either physical obstacles that the robots need to avoid (e.g., walls, other robots, etc.) or illegal states (e.g., all legs off

Ghrist, Robert W.


Perspectives of matrix convex functions  

PubMed Central

In this paper, we generalize the main results of [Effros EG, (2009) Proc Natl Acad. Sci USA 106:1006–1008]. Namely, we provide the necessary and sufficient conditions for jointly convexity of perspective functions and generalized perspective functions.

Ebadian, Ali; Nikoufar, Ismail; Eshaghi Gordji, Madjid



A Fast Method to Minimize L Error Norm for Geometric Vision Problems  

Microsoft Academic Search

Minimizing L? error norm for some geometric vision problems provides global optimization using the well- developed algorithm called SOCP (second order cone programming). Because the error norm belongs to quasi- convex functions, bisection method is utilized to attain the global optimum. It tests the feasibility of the intersection of all the second order cones due to measurements, repeatedly adjusting the

Yongduek Seo; Richard Hartley



The Multiple-Sets Split Feasibility Problem and Its Applications for ...  

E-print Network

Oct 6, 2005 ... closest to a family of closed convex sets in one space such that its ... method to the inverse problem of intensity-modulated radiation therapy (IMRT) ... Projections onto sets are used in a wide variety of methods in optimization ..... the concept of equivalent uniform dose (EUD) was introduced to describe dose.




Electronic neural network for solving traveling salesman and similar global optimization problems  

NASA Technical Reports Server (NTRS)

This invention is a novel high-speed neural network based processor for solving the 'traveling salesman' and other global optimization problems. It comprises a novel hybrid architecture employing a binary synaptic array whose embodiment incorporates the fixed rules of the problem, such as the number of cities to be visited. The array is prompted by analog voltages representing variables such as distances. The processor incorporates two interconnected feedback networks, each of which solves part of the problem independently and simultaneously, yet which exchange information dynamically.

Thakoor, Anilkumar P. (inventor); Moopenn, Alexander W. (inventor); Duong, Tuan A. (inventor); Eberhardt, Silvio P. (inventor)



A hybrid algorithm optimization approach for machine loading problem in flexible manufacturing system  

NASA Astrophysics Data System (ADS)

The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to the relevant machines are made. Such problems are not only combinatorial optimization problems, but also happen to be non-deterministic polynomial-time-hard, making it difficult to obtain satisfactory solutions using traditional optimization techniques. In this paper, an attempt has been made to address the machine loading problem with objectives of minimization of system unbalance and maximization of throughput simultaneously while satisfying the system constraints related to available machining time and tool slot designing and using a meta-hybrid heuristic technique based on genetic algorithm and particle swarm optimization. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as throughput and system utilization.

Kumar, Vijay M.; Murthy, ANN; Chandrashekara, K.



Optimal Taxation in Models of Endogenous Growth  

Microsoft Academic Search

The authors study the problem of optimal taxation in three infinite-horizon, representative-agent endogenous growth models. The first model is a convex model in which physical and human capital are perfectly symmetric. The authors' second model incorporates elastic labor supply through a Lucas-style technology. Analysis of these two models points out the danger of assuming that government expenditures are exogenous. In

Larry E. Jones; Rodolfo E. Manuelli; Peter E. Rossi




PubMed Central

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

Wang, Lan; Kim, Yongdai; Li, Runze