Solving convex problems involving powers using conic optimization
Glineur, FranÃ§ois
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 remarks Future plans CFG 07 Solving convex problems involving powers using conic optimization 2 #12
Convex Optimization Convex Optimization
Masci, Frank
Convex Optimization #12;#12;Convex Optimization Stephen Boyd Department of Electrical Engineering Cataloguing-in-Publication data Boyd, Stephen P. Convex Optimization / Stephen Boyd & Lieven Vandenberghe p. cm. Includes bibliographical references and index. ISBN 0 521 83378 7 1. Mathematical optimization. 2
Mapping the Energy Landscape of Non-Convex Optimization Problems
Zhu, Song Chun
Mapping the Energy Landscape of Non-Convex Optimization Problems Maira Pavlovskaia1 , Kewei Tu2@shanghaitech.edu.cn Abstract. An energy landscape map (ELM) characterizes and visualizes an energy function with a tree the barrier between adjacent energy basins. We demonstrate the utility of ELMs in analyzing non-convex energy
Schittkowski, Klaus
to be efficient tools in the context of mechanical structural optimization, see for instance the comparative studySequential Convex Programming Methods for Solving Large Topology Optimization Problems-scale structural optimization prob- lems by sequential convex programming (SCP). A predictor-corrector interior
Lavaei, Javad
1 Convex Relaxation for Optimal Power Flow Problem: Mesh Networks Ramtin Madani, Somayeh Sojoudi for electrical power networks. This problem, named optimal power flow (OPF), is nonconvex due The optimal power flow (OPF) problem is concerned with finding an optimal operating point of a power system
Lavaei, Javad
1 Convex Relaxation for Optimal Power Flow Problem: Mesh Networks Ramtin Madani, Somayeh Sojoudi and Javad Lavaei Abstract--This paper is concerned with the optimal power flow (OPF) problem. We have. INTRODUCTION The optimal power flow (OPF) problem aims to find an optimal operating point of a power system
Lavaei, Javad
Convex Relaxation for Optimal Power Flow Problem: Mesh Networks Ramtin Madani, Somayeh Sojoudi for electrical power networks. This problem, named optimal power flow (OPF), is nonconvex due The optimal power flow (OPF) problem is concerned with finding an optimal operating point of a power system
Lavaei, Javad
Low-Rank Solution of Convex Relaxation for Optimal Power Flow Problem Somayeh Sojoudi, Ramtin with solving the nonconvex problem of optimal power flow (OPF) via a convex relaxation based on semidefinite problems solved from every few minutes to every several months. State estimation, optimal power flow (OPF
Improving complexity of structured convex optimization problems using self-concordant barriers
Glineur, François
results for several classes of structured convex optimization problems using to the theory of self of introducing two parameters in the definition of self-concordancy and which one is the best to fix. A lemma.Glineur@fpms.ac.be. The author is supported by a grant from the F.N.R.S. (Belgian National Fund for Scientific Research). 1 #12
An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization
Sapatnekar, Sachin
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
Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm
Claus Still; Tapio Westerlund
2006-01-01
In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm\\u000a uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each\\u000a node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step\\u000a is taken
Convex optimization methods for model reduction
Sou, Kin Cheong, 1979-
2008-01-01
Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied.Parameterized ...
An Overview Of Software For Convex Optimization
Borchers, Brian
An Overview Of Software For Convex Optimization Brian Borchers Department of Mathematics New Mexico in this hierarchy up to the level of SDP. · Many other convex optimization problems can be formulated as structured Tech Socorro, NM 87801 borchers@nmt.edu #12;In fact, the great watershed in optimization isn't between
The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications
Xu, Xudan; Zhu, J. Jim; Zhang, Ping
2014-01-01
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
RESEARCH PAPER Convex topology optimization for hyperelastic trusses based
Paulino, Glaucio H.
RESEARCH PAPER Convex topology optimization for hyperelastic trusses based on the ground nonlinear behavior. More specifically, we concentrate on hyperelastic models, such as the ones by Hencky design problem. Keywords Ground structure . Topology optimization . Hyperelasticity . Convex optimization
NATCOR Convex Optimization Linear Programming 1
Hall, Julian
. Hall NATCOR Convex Optimization: Linear Programming 1 2 / 1 Overview What is LP? General LP problemsNATCOR Convex Optimization Linear Programming 1 Julian Hall School of Mathematics University a result which Is nice in itself Leads into "Structure and matrix sparsity": Wednesday 13:3015:30 J. A. J
Henrion, Didier
A review of the book "Functional analysis and applied optimization in Banach spaces - Applications to non-convex variational problems" by Fabio Botelho, Springer, Cham, Switzerland, 2014. The book extensively in the landmark book [I. Ekeland, R. Temam. Convex analysis and variational problems. Elsevier
Stochastic Convex Optimization with Multiple Objectives
Jin, Rong
Stochastic Convex Optimization with Multiple Objectives Mehrdad Mahdavi Michigan State University and stochasticity in the first-order information. We cast the stochastic multi- ple objective optimization problem first approximates the stochastic objectives by sampling and then solves a constrained stochastic
Convex Optimization of Graph Laplacian Eigenvalues
Convex Optimization of Graph Laplacian Eigenvalues Stephen Boyd Abstract. We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constraints on the weights
Subset of routes for OD pair k O2 nk = Rk Number of routes for OD pair k fk Rnk Flow (vehicle count) measured for OD pair k xk [0, 1]nk xk r is the portion of flow fk directed to route r Rk Ak R|L|×nk Corresponding block of nk columns of A 6/30 #12;INTRODUCTION PROBLEM FORMULATION METHODOLOGY DUALITY Algorithms
1 Convex Optimization with Sparsity-Inducing Norms
Bach, Francis
estimation as convex optimization problems has two main benefits: First, it leads to efficient estimation algorithms--and this chapter focuses primarily on these. Second, it allows a fruitful theoretical analysis. This chapter is organized as follows: in Section 1.1.1, we present the optimization problems related to sparse
An interior-point Lagrangian decomposition method for separable convex optimization
An interior-point Lagrangian decomposition method for separable convex optimization I. Necoara1 it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm convex problems. Keywords. Separable convex optimization, self-concordant function, interior
Murota, Kazuo
systems. · In network flow problems, flow and tension are dual objects. Roughly speak- ing, flow, for example, the differential operator corresponds to L-convexity and the Green function to M and convex functions through a variety of examples of discrete systems and the axiomatic approach presented
Lavaei, Javad
1 Abstract-- The optimal power flow (OPF) problem is a critical problem for power generation part of a complex matrix Im: imaginary part of a complex matrix II. INTRODUCTION The optimal power flow problem was first discussed in Carpentier's paper [1] in 1962. The objective of an Optimal Power Flow (OPF
Robust boosting via convex optimization
NASA Astrophysics Data System (ADS)
Rätsch, Gunnar
2001-12-01
In this work we consider statistical learning problems. A learning machine aims to extract information from a set of training examples such that it is able to predict the associated label on unseen examples. We consider the case where the resulting classification or regression rule is a combination of simple rules - also called base hypotheses. The so-called boosting algorithms iteratively find a weighted linear combination of base hypotheses that predict well on unseen data. We address the following issues: o The statistical learning theory framework for analyzing boosting methods. We study learning theoretic guarantees on the prediction performance on unseen examples. Recently, large margin classification techniques emerged as a practical result of the theory of generalization, in particular Boosting and Support Vector Machines. A large margin implies a good generalization performance. Hence, we analyze how large the margins in boosting are and find an improved algorithm that is able to generate the maximum margin solution. o How can boosting methods be related to mathematical optimization techniques? To analyze the properties of the resulting classification or regression rule, it is of high importance to understand whether and under which conditions boosting converges. We show that boosting can be used to solve large scale constrained optimization problems, whose solutions are well characterizable. To show this, we relate boosting methods to methods known from mathematical optimization, and derive convergence guarantees for a quite general family of boosting algorithms. o How to make Boosting noise robust? One of the problems of current boosting techniques is that they are sensitive to noise in the training sample. In order to make boosting robust, we transfer the soft margin idea from support vector learning to boosting. We develop theoretically motivated regularized algorithms that exhibit a high noise robustness. o How to adapt boosting to regression problems? Boosting methods are originally designed for classification problems. To extend the boosting idea to regression problems, we use the previous convergence results and relations to semi-infinite programming to design boosting-like algorithms for regression problems. We show that these leveraging algorithms have desirable theoretical and practical properties. o Can boosting techniques be useful in practice? The presented theoretical results are guided by simulation results either to illustrate properties of the proposed algorithms or to show that they work well in practice. We report on successful applications in a non-intrusive power monitoring system, chaotic time series analysis and a drug discovery process. --- Anmerkung: Der Autor ist Träger des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2001/2002. In dieser Arbeit werden statistische Lernprobleme betrachtet. Lernmaschinen extrahieren Informationen aus einer gegebenen Menge von Trainingsmustern, so daß sie in der Lage sind, Eigenschaften von bisher ungesehenen Mustern - z.B. eine Klassenzugehörigkeit - vorherzusagen. Wir betrachten den Fall, bei dem die resultierende Klassifikations- oder Regressionsregel aus einfachen Regeln - den Basishypothesen - zusammengesetzt ist. Die sogenannten Boosting Algorithmen erzeugen iterativ eine gewichtete Summe von Basishypothesen, die gut auf ungesehenen Mustern vorhersagen. Die Arbeit behandelt folgende Sachverhalte: o Die zur Analyse von Boosting-Methoden geeignete Statistische Lerntheorie. Wir studieren lerntheoretische Garantien zur Abschätzung der Vorhersagequalität auf ungesehenen Mustern. Kürzlich haben sich sogenannte Klassifikationstechniken mit großem Margin als ein praktisches Ergebnis dieser Theorie herausgestellt - insbesondere Boosting und Support-Vektor-Maschinen. Ein großer Margin impliziert eine hohe Vorhersagequalität der Entscheidungsregel. Deshalb wird analysiert, wie groß der Margin bei Boosting ist und ein verbesserter Algorithmus vorgeschl
Convex Optimization of Graph Laplacian Eigenvalues
unfolding Â· conclusions #12;(Weighted) graph Laplacian Â· graph G = (V, E) with n = |V | nodes, m = |E| edges = 1 edge l enters node i -1 edge l leaves node i 0 otherwise Â· (weighted) Laplacian: L = A diagConvex Optimization of Graph Laplacian Eigenvalues Stephen Boyd Stanford University (Joint work
Glineur, FranÃ§ois
constraints: Structured convex optimization (convexity by design) Reward for a convex formulation Â·Full Screen Â·Close Â·Quit Overview of the thesis Interior-point methods Linear optimization survey Self Back Â·Full Screen Â·Close Â·Quit Overview of this talk Interior-point methods Linear optimization survey
Glineur, FranÃ§ois
work with specific classes of convex constraints: Structured convex optimization (convexity by design Optimization Â·First Â·Prev Â·Next Â·Last Â·Go Back Â·Full Screen Â·Close Â·Quit Overview of the thesis Interior in Convex Optimization Â·First Â·Prev Â·Next Â·Last Â·Go Back Â·Full Screen Â·Close Â·Quit Overview of this talk
MODERN CONVEX OPTIMIZATION Arkadi Nemirovski
Moreno Maza, Marc
. Well, the same is with the wheel. In 50 plus years since its birth, Mathematical Programming can be outlined as follows: Realizing what are the generic optimization programs one can solve well optimization programs we can solve well": #12;3 (!) As far as numerical processing of programs (P) is concerned
Problems of unboundedness of convex functions
Obuchowska, W.; Murty, K.G.
1994-12-31
We consider the problem of determining whether or not a convex function is bounded below. We propose an algorithm to determine the direction in the cone of recession along which the function is unbounded and we show that for some classes of functions unboundedness implies existence of the direction of unboundness. Also we present examples of functions, which are unbounded below, but bounded along any direction vector.
Lagrange duality theory for convex control problems
NASA Technical Reports Server (NTRS)
Hager, W. W.; Mitter, S. K.
1976-01-01
The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.
On the Design of Optimal Structured and Sparse Feedback Gains via Sequential Convex Programming
Jovanovic, Mihailo
On the Design of Optimal Structured and Sparse Feedback Gains via Sequential Convex Programming attention has been paid to the problem of optimal structured control in [16][18], where the H2-norm Makan Fardad and Mihailo R. Jovanovi´c Abstract-- We consider the problem of finding optimal feed- back
Yu, Wei
problem is cast into a convex form, the structure of the optimal solution, which often reveals design of this tutorial provides an overview of these developments and describes the basic optimization concepts, models to Convex Optimization for Communications and Signal Processing Zhi-Quan Luo, Senior Member, IEEE, and Wei
An extended cutting plane method for solving convex MINLP problems
Tapio Westerlund; Frank Pettersson
1995-01-01
An extended version of Kelley's cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley's cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP problems with a
From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation
Egozcue, J. Meziat, R. Pedregal, P.
2002-12-19
We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.
Phase retrieval using iterative Fourier transform and convex optimization algorithm
NASA Astrophysics Data System (ADS)
Zhang, Fen; Cheng, Hong; Zhang, Quanbing; Wei, Sui
2015-05-01
Phase is an inherent characteristic of any wave field. Statistics show that greater than 25% of the information is encoded in the amplitude term and 75% of the information is in the phase term. The technique of phase retrieval means acquire phase by computation using magnitude measurements and provides data information for holography display, 3D field reconstruction, X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Mathematically, solving phase retrieval problem is an inverse problem taking the physical and computation constraints. Some recent algorithms use the principle of compressive sensing, such as PhaseLift, PhaseCut and compressive phase retrieval etc. they formulate phase retrieval problems as one of finding the rank-one solution to a system of linear matrix equations and make the overall algorithm a convex program over n × n matrices. However, by "lifting" a vector problem to a matrix one, these methods lead to a much higher computational cost as a result. Furthermore, they only use intensity measurements but few physical constraints. In the paper, a new algorithm is proposed that combines above convex optimization methods with a well known iterative Fourier transform algorithm (IFTA). The IFTA iterates between the object domain and spectral domain to reinforce the physical information and reaches convergence quickly which has been proved in many applications such as compute-generated-hologram (CGH). Herein the output phase of the IFTA is treated as the initial guess of convex optimization methods, and then the reconstructed phase is numerically computed by using modified TFOCS. Simulation results show that the combined algorithm increases the likelihood of successful recovery as well as improves the precision of solution.
Convex Optimization Approaches for Blind Sensor Calibration Using Sparsity
NASA Astrophysics Data System (ADS)
Bilen, Cagdas; Puy, Gilles; Gribonval, Remi; Daudet, Laurent
2014-09-01
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided.
Kernel regression for travel time estimation via convex optimization
Kernel regression for travel time estimation via convex optimization Sébastien Blandin , Laurent El Ghaoui and Alexandre Bayen Abstract--We develop an algorithm aimed at estimating travel time on segments of a road network using a convex optimiza- tion framework. Sampled travel time from probe vehicles
Spacecraft Swarm Guidance Using a Sequence of Decentralized Convex Optimizations
Chung, Soon-Jo
Spacecraft Swarm Guidance Using a Sequence of Decentralized Convex Optimizations Daniel Morgan Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA This paper presents partially decentralized path planning algorithms for swarms of spacecraft composed of hundreds to thousands
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian
Instituto de Sistemas e Robotica
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x = x with a novel distributed, decentralized algorithm. We refer to this algorithm as ALG (augmented Lagrangian
Motion Planning with Sequential Convex Optimization and Convex Collision Checking
Patil, Sachin
3D-printed implants for intracavitary brachytherapy. Details, videos, and source code is freely trajectories, and (f) optimized layout for bounded curvature channels within 3D-printed vaginal implants and the environments that they operate in has spurred the need for high-dimensional motion planning. Consider
Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding
Pratt, Vaughan
vi(Si). The second problem is welfare maximization in combinatorial public projects (CPPs). HereOptimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding-in-expectation, constant-factor approximation mechanisms for NP-hard cases of the welfare maximization problem
August 2000 (Convex Optimization ) JP Goux The mega title ...
Implicitly defined barrier functions: elementary properties and applications ... James V. Burke , Adrian S. Lewis , Michael L. Overton ... John E Mitchell , Srinivasan Ramaswamy ... Convex- and Monotone- Transformable Mathematical Programming Problems and a Proximal-Like Point ... Alexandre Belloni , Robert M. Freund
FIR Filter Design via Spectral Factorization and Convex Optimization 1 FIR Filter Design via UCSB 10 24 97 FIR Filter Design via Spectral Factorization and Convex Optimization 2 Outline Convex Spectral factorization methods Discretization #12;FIR Filter Design via Spectral Factorization and Convex
Convex Optimization in Julia Madeleine Udell
. The Julia language [6] is a high-level, high-performance dynamic programming language for technical Languages Keywords Convex programming, automatic verification, symbolic com- putation, multiple dispatch 1 package to write extremely performant code using a high level of abstrac- tion. Indeed, the abstraction
Regularization Constants in LS-SVMs: a Fast Estimate via Convex Optimization
Regularization Constants in LS-SVMs: a Fast Estimate via Convex Optimization Kristiaan Pelckmans Support Vector Machines (LS-SVMs) for regression and classification is considered. The formulation of the LS-SVM training and regularization constant tuning problem (w.r.t. the validation performance
FAST CONVEX OPTIMIZATION ALGORITHMS FOR EXACT RECOVERY OF A CORRUPTED LOW-RANK MATRIX
Liberzon, Daniel
FAST CONVEX OPTIMIZATION ALGORITHMS FOR EXACT RECOVERY OF A CORRUPTED LOW-RANK MATRIX ZHOUCHEN LIN for solving the problem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted the data are corrupted by small Gaussian noise, it breaks down under large corruption, even
Convex Optimization: Fall 2013 Machine Learning 10-725/Statistics 36-725
Tibshirani, Ryan
Convex Optimization: Fall 2013 Machine Learning 10-725/Statistics 36-725 Instructors: Barnabas Poczos, Dept. of Machine Learning, bapoczos@cs.cmu.edu Ryan Tibshirani, Dept. of Statistics, ryantibs and objectives Nearly every problem in machine learning and statistics can be formulated in terms
Convex optimization under inequality constraints in rank-deficient systems
NASA Astrophysics Data System (ADS)
Roese-Koerner, Lutz; Schuh, Wolf-Dieter
2014-05-01
Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.
Distributed NonAutonomous Power Control through Distributed Convex Optimization
Sundhar Srinivasan Ram; Venugopal V. Veeravalli; Angelia Nedic
2009-01-01
We consider the uplink power control problem where mobile users in different cells are communicating with their base stations. We formulate the power control problem as the minimization of a sum of convex functions. Each component function depends on the channel coefficients from all the mob ile users to a specific base station and is assumed to be known only
Research Study on Convex Optimization of Power Distribution Networks
Lavaei, Javad
and power production range of a generator and so on. We would first use a two-bus system as an exampleResearch Study on Convex Optimization of Power Distribution Networks Ying Teng, UNI: yt2351 I communication and control technology impels the transformation of power distribution system in both its
The inverse moment problem for convex polytopes
Gravin, Nick; Pasechnik, Dmitrii; Robins, Sinai
2011-01-01
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.
Low, Steven H.
IEEE TRANS. ON AUTOMATIC CONTROL, 2014 (TO APPEAR) 1 Exact Convex Relaxation of Optimal Power Flow in Radial Networks Lingwen Gan, Na Li, Ufuk Topcu, and Steven H. Low Abstract--The optimal power flow (OPF networks and two real-world networks. I. INTRODUCTION The optimal power flow (OPF) problem determines a net
Sapatnekar, Sachin
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
Low, Steven H.
recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural SYSTEMS, JUNE 2014 (WITH PROOFS) 3 I. INTRODUCTION The optimal power flow (OPF) problem is fundamental Power Flow Part II: Exactness Steven H. Low Electrical Engineering, Computing+Mathematical Sciences
Low, Steven H.
--This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem an optimal power flow (OPF) problem is a mathematical program that seeks to minimize a certain function Power Flow Part I: Formulations and Equivalence Steven H. Low EAS, Caltech slow@caltech.edu Abstract
M. J. Cánovas; A. Hantoute; M. A. López; J. Parra
2008-01-01
This paper deals with a parametric family of convex semi-infinite optimization problems for which linear perturbations of\\u000a the objective function and continuous perturbations of the right-hand side of the constraint system are allowed. In this context,\\u000a Cánovas et al. (SIAM J. Optim. 18:717–732, [2007]) introduced a sufficient condition (called ENC in the present paper) for the strong Lipschitz stability of
On An Evolution Problem For Convex Curves Lishang Jiang
On An Evolution Problem For Convex Curves Lishang Jiang and more circular during the evolution process, and the final shape of the evolving curve will be a circle. What happens to a curve X0(u) as it flows in this way? Some facts * *of the flow are rather straight
MODERN CONVEX OPTIMIZATION Aharon Ben-Tal
Nemirovski, Arkadi
optimization programs one can solve well ("efficiently solv- able" programs) and when such a possibility is, not well posed!) "what are generic optimization programs we can solve well": #12;3 (!) As far as numerical.isye.gatech.edu/faculty-staff/profile.php?entry=an63 Fall Semester 2013 #12;2 Preface Mathematical Programming deals with optimization programs
Structural analysis of complex ecological economic optimal control problems
T. Kiseleva
2011-01-01
This thesis demonstrates the importance and effectiveness of methods of bifurcation theory applied to studying non-convex optimal control problems. It opens up a new methodological approach to investigation of parameterized economic models. While standard analytical methods are not efficient and sometimes impossible to apply to non-convex problems, the numerical geometrical methods developed in the thesis allow to solve and analyze
A partially inexact bundle method for convex semi-infinite minmax problems
NASA Astrophysics Data System (ADS)
Fuduli, Antonio; Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna
2015-04-01
We present a bundle method for solving convex semi-infinite minmax problems which allows inexact solution of the inner maximization. The method is of the partially inexact oracle type, and it is aimed at reducing the occurrence of null steps and at improving bundle handling with respect to existing methods. Termination of the algorithm is proved at a point satisfying an approximate optimality criterion, and the results of some numerical experiments are also reported.
Analysis of the Criteria of Activation-Based Inverse Electrocardiography using Convex Optimization
Erem, Burak; van Dam, Peter M.; Brooks, Dana H.
2012-01-01
In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. However, in experiments conducted on a subject with Wolff-Parkinson-White syndrome, we have observed that there may be a mismatch between favorable solutions of the optimization problem and solutions with the desired physiological characteristics. In this work, we use a method based on a convex optimization framework to explore the solution space and analyze whether the optimization criteria target their intended objective. PMID:22255195
Analysis of the criteria of activation-based inverse electrocardiography using convex optimization.
Erem, Burak; van Dam, Peter M; Brooks, Dana H
2011-01-01
In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. However, in experiments conducted on a subject with Wolff-Parkinson-White syndrome, we have observed that there may be a mismatch between favorable solutions of the optimization problem and solutions with the desired physiological characteristics. In this work, we use a method based on a convex optimization framework to explore the solution space and analyze whether the optimization criteria target their intended objective. PMID:22255195
Studies integrating geometry, probability, and optimization under convexity
Nogueira, Alexandre Belloni
2006-01-01
Convexity has played a major role in a variety of fields over the past decades. Nevertheless, the convexity assumption continues to reveal new theoretical paradigms and applications. This dissertation explores convexity ...
Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
Girard, Julien N; Starck, Jean Luc; Corbel, Stéphane; Woiselle, Arnaud; Tasse, Cyril; McKean, John P; Bobin, Jérôme
2015-01-01
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emissions as compared to CLEAN. With the advent of large radiotel...
Hybrid Random/Deterministic Parallel Algorithms for Convex and Nonconvex Big Data Optimization
NASA Astrophysics Data System (ADS)
Daneshmand, Amir; Facchinei, Francisco; Kungurtsev, Vyacheslav; Scutari, Gesualdo
2015-08-01
We propose a decomposition framework for the parallel optimization of the sum of a differentiable {(possibly nonconvex)} function and a nonsmooth (possibly nonseparable), convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. The main contribution of this work is a novel \\emph{parallel, hybrid random/deterministic} decomposition scheme wherein, at each iteration, a subset of (block) variables is updated at the same time by minimizing local convex approximations of the original nonconvex function. To tackle with huge-scale problems, the (block) variables to be updated are chosen according to a \\emph{mixed random and deterministic} procedure, which captures the advantages of both pure deterministic and random update-based schemes. Almost sure convergence of the proposed scheme is established. Numerical results show that on huge-scale problems the proposed hybrid random/deterministic algorithm outperforms both random and deterministic schemes.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yin, Chuancun; Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process.
Yin, Chuancun; Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
NASA Astrophysics Data System (ADS)
Girard, J. N.; Garsden, H.; Starck, J. L.; Corbel, S.; Woiselle, A.; Tasse, C.; McKean, J. P.; Bobin, J.
2015-08-01
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ? 2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.
Gálvez, Akemi; Iglesias, Andrés
2013-01-01
Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380
Gálvez, Akemi; Iglesias, Andrés
2013-01-01
Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380
CONTROL OF A CLIMBING ROBOT USING REAL-TIME CONVEX OPTIMIZATION
is closed around desired robot chassis position to generate cartesian feedback forces. A convex optimizationCONTROL OF A CLIMBING ROBOT USING REAL-TIME CONVEX OPTIMIZATION Teresa G. Miller Timothy W. Bretl Abstract: This paper presents a controller for a free-climbing robot. Given a pre-planned path, a loop
Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem.
Al-Mulhem, M; Al-Maghrabi, T
1998-01-01
This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions. PMID:18255981
Improving beampatterns of two-dimensional random arrays using convex optimization
Gerstoft, Peter
Improving beampatterns of two-dimensional random arrays using convex optimization Peter Gerstofta the locations are non-optimal from a beamforming perspective. The loca- tion of each senor is accurately known
Glineur, François
Fran¸cois Glineur, Advances in Structured Convex Optimization - 1 - ·First ·Prev ·Next ·Last ·Full Screen ·Quit Recent Advances in Structured Convex Optimization Fran¸cois Glineur Charg´e de Recherches F, Advances in Structured Convex Optimization - 2 - ·First ·Prev ·Next ·Last ·Full Screen ·Quit Motivation
Lu, Xin, Ph. D. Massachusetts Institute of Technology. Operations Research Center
2013-01-01
In this thesis, we study online optimization problems in routing and allocation applications. Online problems are problems where information is revealed incrementally, and decisions must be made before all information is ...
Low, Steven H.
of Optimal Power Flow Part I: Formulations and Equivalence Steven H. Low Electrical Engineering, Computing summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing III Optimal power flow 8 III-A Bus injection model
Online Convex Optimization with Ramp Constraints Masoud Badiei, Na Li, Adam Wierman
Wierman, Adam
Online Convex Optimization with Ramp Constraints Masoud Badiei, Na Li, Adam Wierman Harvard@caltech.edu Abstract--We study a novel variation of online convex opti- mization where the algorithm is subject to ramp between consecutive actions, i.e., is subject to ramp constraints. In particular, we consider a setting
A Convex Framework for Optimal Investment on Disease Awareness in Social Networks
Preciado, Victor M; Scoglio, Caterina
2013-01-01
We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary network of contacts by investing on disease awareness throughout the network. We model the effect of agent awareness on the dynamics of an epidemic using the SAIS epidemic model, an extension of the SIS epidemic model that includes a state of "awareness". This model allows to derive a condition to control the spread of an epidemic outbreak in terms of the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the cost-optimal investment on disease awareness throughout the network when the cost function presents some realistic properties. We propose a convex framework to find cost-optimal allocation of resources. We validate our results with numerical simulations in a real online social network.
DEMOS for OPTIMIZATION Problems
NSDL National Science Digital Library
Roberts, Lila F.
2002-09-16
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.
Implementation of a Point Algorithm for Real-Time Convex Optimization
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Motaghedi, Shui; Carson, John
2007-01-01
The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.
Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model
Vera Andreo, Jorge R.
Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation oracle with no further information (e.g., no domain ball containing or intersecting the set, etc.). The authors' ...
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
Agarwal, Alekh
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 ...
Tractable problems in optimal decentralized control
NASA Astrophysics Data System (ADS)
Rotkowitz, Michael Charles
2005-07-01
This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.
On Projection Algorithms for Solving Convex Feasibility Problems
Heinz H. Bauschke; Jonathan M. Borwein
1996-01-01
Due to their extraordinary utility and broad applicability in many areasof classical mathematics and modern physical sciences (most notably,computerized tomography), algorithms for solving convex feasibilityproblems continue to receive great attention. To unify, generalize, andreview some of these algorithms, a very broad and flexible frameworkis investigated . Several crucial new concepts which allow a systematicdiscussion of questions on behaviour in general
Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir
2014-11-01
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
An outer approximation based branch and cut algorithm for convex 0-1 MINLP problems
Berc Rustem; Ioannis Akrotirianakis; Istvan Maros
2001-01-01
A branch and cut algorithm is developed for solving convex 0-1 Mixed Integer Nonlinear Programming (MINLP) problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints
Orthogonal projections onto convex sets and the application to problems in plasticity
Wieners, Christian
Orthogonal projections onto convex sets and the application to problems in plasticity Christian Wieners ABSTRACT. We review the classical theory of static and quasiÂstatic plasticity in an abstract problem in plasticity. The abstract setting is applied to problems in perfect plasticity and to plasticity
Higher order sensitivity of solutions to convex programming problems without strict complementarity
NASA Technical Reports Server (NTRS)
Malanowski, Kazimierz
1988-01-01
Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.
Trees with Convex Faces and Optimal Angles David Eppstein
Eppstein, David
= consecutive subsequence of trees descending from children of some node forming the pattern: path Â (0 or more(#descendants of top vertex) #12;Convex trees Carlson & Eppstein, GD 2006 Edge Lengths chosen so vertices lie trees? Force all slopes to lie in a 180-degree arc Same methods should extend straightforwardly Other
Convex Optimization of Coincidence Time Resolution for a High-Resolution PET System
Reynolds, Paul D.; Olcott, Peter D.; Pratx, Guillem; Lau, Frances W. Y.
2013-01-01
We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3’s analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n3) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ± 0.07 ns full-width at half-maximum (FWHM) to 6.92 ± 0.02 ns FWHM (11.52 ± 0.05 ns to 4.89 ± 0.02 ns for unpaired photons). PMID:20876008
Distributed Algorithms for Optimal Power Flow Problem
Lam, Albert Y S; Tse, David
2011-01-01
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured...
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
Gan, LW; Li, N; Topcu, U; Low, SH
2015-01-01
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.
The role of convexity for solving some shortest path problems in plane without triangulation
NASA Astrophysics Data System (ADS)
An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van
2013-09-01
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.
Optimal Power Flow Based Demand Response Offer Price Optimization
Lavaei, Javad
Optimal Power Flow Based Demand Response Offer Price Optimization Zhen Qiu 1 Introduction significantly decrease the costs. The optimal power flow problem is non-convex in general. We formulate convex
libCreme: An optimization library for evaluating convex-roof entanglement measures
NASA Astrophysics Data System (ADS)
Röthlisberger, Beat; Lehmann, Jörg; Loss, Daniel
2012-01-01
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:http://cpc.cs.qub.ac.uk/summaries/AEKD_v1_0.html 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.
Convergent LMI relaxations for non-convex optimization over polynomials in control
Henrion, Didier
with parametric uncertainty, simultaneous stabilization of linear systems, pole assignment by static outputConvergent LMI relaxations for non-convex optimization over polynomials in control Didier Henrion and constraints [1]. Typical examples include robust stability analysis for char- acteristic polynomials
Temperature Control of High-Performance Multi-core Platforms Using Convex Optimization
De Micheli, Giovanni
Temperature Control of High-Performance Multi-core Platforms Using Convex Optimization Srinivasan.demicheli}@epfl.ch, {almirm, boyd}@stanford.edu, Â§ rgupta@ucsd.edu, Â¶ lbenini@deis.unibo.it ABSTRACT With technology advances to a significant increase in chip temperature. Temperature gradi- ents and hot-spots not only affect
10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method
Tibshirani, Ryan
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 such that f(x ) = 0. Figure 9.1 illustrates another motivation of Newton method. Given a function f, we want
Adapted Convex Optimization Algorithm for Wavelet-Based Dynamic PET Reconstruction
Paris-Sud XI, Université de
1 Adapted Convex Optimization Algorithm for Wavelet-Based Dynamic PET Reconstruction Nelly Abstract--This work deals with Dynamic Positron Emission Tomography (PET) data reconstruction, considering. The effectiveness of this approach is shown with simulated dynamic PET data. Comparative results are also provided
ON THE RELATION BETWEEN OPTION AND STOCK PRICES: A CONVEX OPTIMIZATION APPROACH
Bertsimas, Dimitris
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 that are affected by multiple stocks either directly (the payoff of the option depends on multiple stocks
Temperature-Aware Processor Frequency Assignment for MPSoCs Using Convex Optimization
Gupta, Rajesh
are met. We perform experiments on several realistic SoC benchmarks using a cycle-accurate FPGA Business analysts forecast a 200 billion dollar market for media- rich, mobile System-on-Chip (SoCTemperature-Aware Processor Frequency Assignment for MPSoCs Using Convex Optimization Srinivasan
Monotonicity and stability of optimal solutions of a minimization problem
NASA Astrophysics Data System (ADS)
Liu, Yichen; Emamizadeh, Behrouz
2015-08-01
This paper is concerned with a minimization problem modeling the minimum displacement of an isotropic elastic membrane subject to a vertical force such as a load distribution. In addition to proving existence and uniqueness of optimal solutions, we show that these solutions are monotone and stable, in a certain sense. The main mathematical tool used in the analysis is the tangent cones from convex analysis, which helps to derive the optimality condition. Our results are compatible with physical expectations.
Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China)] [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China)] [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China)] [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States) [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)] [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)
2014-04-15
Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT segmentation based on 15 patients.
Roland T. Chin
1994-01-01
A morphological operation using a large structuring element can be decomposed equivalently into a sequence of recursive operations, each using a smaller structuring element. However, an optimal decomposition of arbitrarily shaped structuring elements is yet to be found. In this paper, we have derived an optimal decomposition of a specific class of structuring elements\\/spl mdash\\/convex sets\\/spl mdash\\/for a specific type
CONVEXITY PROPERTIES OF INVERSE PROBLEMS WITH VARIATIONAL CONSTRAINTS
of mathematical physics, feasibility constraints can be found for the nonlinear inversion problem of the variational problems of mathematical physics, rigorous physically based feasibility (or admissibility of the particular choice of discretization made in practical algorithms for solving the inverse problem
NON-CONVEX SPARSE OPTIMIZATION THROUGH DETERMINISTIC ANNEALING AND APPLICATIONS
Granada, Universidad de
provides locally optimal solutions. In addition, to avoid non-favorable minima we use an annealing authors funded by grant TEC2006/13845/TCM from the Ministerio de Ciencia y TecnologÂ´ia, Spain. technique
Chintala, Rohit
2012-10-19
Numerical methods of designing control systems are currently an active area of research. Convex optimization with linear matrix inequalities (LMIs) is one such method. Control objectives like minimizing the H_2, H_infinity norms, limiting...
The convex algebraic geometry of linear inverse problems
Chandrasekaran, Venkat
We study a class of ill-posed linear inverse problems in which the underlying model of interest has simple algebraic structure. We consider the setting in which we have access to a limited number of linear measurements of ...
Class and Home Problems: Optimization Problems
ERIC Educational Resources Information Center
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
NASA Technical Reports Server (NTRS)
Oakley, Celia M.; Barratt, Craig H.
1990-01-01
Recent results in linear controller design are used to design an end-point controller for an experimental two-link flexible manipulator. A nominal 14-state linear-quadratic-Gaussian (LQG) controller was augmented with a 528-tap finite-impulse-response (FIR) filter designed using convex optimization techniques. The resulting 278-state controller produced improved end-point trajectory tracking and disturbance rejection in simulation and experimentally in real time.
Interior point decoding for linear vector channels based on convex optimization
Tadashi Wadayama
2010-01-01
In the present paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, which is referred to hereinafter as interior point decoding, is designed for linear vector channels. The linear vector channels include several practically important channels, such as inter-symbol interference channels and partial response (PR) channels. It is shown that
Dynamic Planar Convex Hull with Optimal Query Time and O(log n log log n) Update Time
Riko Jacob
Dynamic Planar Convex Hull with Optimal Query Time and O(log n #1; log log n) Update Time Gerth St supporting point inser- tions in amortized O(log n #1; log log log n) time, point deletions in amor- tized O(log n #1; log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time
Craft, David
2009-01-01
A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. PMID:20022275
Convex and Discrete Geometry: Ideas, Problems and Peter M. Gruber
Gruber, Peter M.
semigroup with cancellation law. A major problem of the Brunn-Minkowski theory is to obtain information on the volume V (C + D) of C + D in terms of information on C and D. The first pertinent result is Steiner's formula for the volume of parallel bodies (1840). Let Bd be the solid Euclidean unit ball of Ed
Nonnegative Mixed-Norm Convex Optimization for Mitotic Cell Detection in Phase Contrast Microscopy
Hao, Tong; Gao, Zan; Su, Yuting; Yang, Zhaoxuan
2013-01-01
This paper proposes a nonnegative mix-norm convex optimization method for mitotic cell detection. First, we apply an imaging model-based microscopy image segmentation method that exploits phase contrast optics to extract mitotic candidates in the input images. Then, a convex objective function regularized by mix-norm with nonnegative constraint is proposed to induce sparsity and consistence for discriminative representation of deformable objects in a sparse representation scheme. At last, a Support Vector Machine classifier is utilized for mitotic cell modeling and detection. This method can overcome the difficulty in feature formulation for deformable objects and is independent of tracking or temporal inference model. The comparison experiments demonstrate that the proposed method can produce competing results with the state-of-the-art methods. PMID:24348733
Nonnegative mixed-norm convex optimization for mitotic cell detection in phase contrast microscopy.
Liu, Anan; Hao, Tong; Gao, Zan; Su, Yuting; Yang, Zhaoxuan
2013-01-01
This paper proposes a nonnegative mix-norm convex optimization method for mitotic cell detection. First, we apply an imaging model-based microscopy image segmentation method that exploits phase contrast optics to extract mitotic candidates in the input images. Then, a convex objective function regularized by mix-norm with nonnegative constraint is proposed to induce sparsity and consistence for discriminative representation of deformable objects in a sparse representation scheme. At last, a Support Vector Machine classifier is utilized for mitotic cell modeling and detection. This method can overcome the difficulty in feature formulation for deformable objects and is independent of tracking or temporal inference model. The comparison experiments demonstrate that the proposed method can produce competing results with the state-of-the-art methods. PMID:24348733
Fast and optimal solution for the generalized attitude determination problem
NASA Astrophysics Data System (ADS)
Ghosh, Arnab
This thesis provides a fast and optimal approach to solve Wahba's general weighted problem. Applications of Wahba's general weighted problem involve attitude determination using wide field-of-view sensors or GPS sensor observations. The first approach developed applies a homotopy continuation based solver to find the global minimizer of the minimization problem. This approach first finds all the stationary points of the minimization problem by solving the polynomial equations satisfied by the stationary points and then chooses the global minimizer from them. Next, a second approach is discussed, based on solving an unconstrained optimization problem using an iterative Newton solution. The parameter space includes the attitude and lagrange multipliers. The initial guess for Newton's method is calculated by approximating the Wahba's general weighted cost and constraints to a convex form and applying semidefinite programming to have global optimum attitude. Monte Carlo-based simulation results indicate that convergence is given quickly to the optimal solution.
A Problem on Optimal Transportation
ERIC Educational Resources Information Center
Cechlarova, Katarina
2005-01-01
Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…
Nonlinear and linear entanglement witnesses for bipartite systems via exact convex optimization
M. A. Jafarizadeh; A. Heshmati; K. Aghayara
2009-10-28
Linear and nonlinear entanglement witnesses for a given bipartite quantum systems are constructed. Using single particle feasible region, a way of constructing effective entanglement witnesses for bipartite systems is provided by exact convex optimization. Examples for some well known two qutrit quantum systems show these entanglement witnesses in most cases, provide necessary and sufficient conditions for separability of given bipartite system. Also this method is applied to a class of bipartite qudit quantum systems with details for d=3, 4 and 5. Keywords: non-linear and linear entanglement witnesses PACS number(s): 03.67.Mn, 03.65.Ud
A Weiszfeld-like algorithm for a Weber location problem constrained to a closed and convex set
Torres, Germán A
2012-01-01
The Weber problem consists of finding a point in $\\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed point iteration. In this work a Weber problem constrained to a closed and convex set is considered. A Weiszfeld-like algorithm, well defined even when an iterate is a vertex, is presented. The iteration function $Q$ that defines the proposed algorithm, is based mainly on an orthogonal projection over the feasible set, combined with the iteration function of the modified Weiszfeld algorithm presented by Vardi and Zhang in 2001. It can be proved that $x^*$ is a fixed point of the iteration function $Q$ if and only if $x^*$ is the solution of the constrained Weber problem. Besides that, under certain hypotheses, $x^*$ satisfies the KKT optimali...
Convex formulations of inverse modeling problems on systems modeled by Hamilton-Jacobi equations modeling problems on systems modeled by Hamilton-Jacobi equations. Applications to traffic flow engineering modeling problems on systems modeled by Hamilton-Jacobi equations. Applications to traffic flow engineering
CONVEXIFICATION OF GENERALIZED NETWORK FLOW PROBLEM WITH APPLICATION TO POWER SYSTEMS
Lavaei, Javad
. Recent work on the optimal power flow (OPF) problem has shown that this non-convex problem can be solved, convex relaxation, electrical power network, optimal power flow AMS subject classifications. 05C21, 90C25
About an Optimal Visiting Problem
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)
2012-02-15
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.
NASA Astrophysics Data System (ADS)
Hoffmann, Aswin L.; den Hertog, Dick; Siem, Alex Y. D.; Kaanders, Johannes H. A. M.; Huizenga, Henk
2008-11-01
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.
ON VERIFIED NUMERICAL COMPUTATIONS IN CONVEX PROGRAMMING CHRISTIAN JANSSON
Jansson, Christian
, a natural non-smooth extension of linear programming. There, the problem is to minimize a linear functionON VERIFIED NUMERICAL COMPUTATIONS IN CONVEX PROGRAMMING CHRISTIAN JANSSON Abstract. This survey-smooth convex conic optimization in the framework of functional analysis, for linear programming
convex segmentation and mixed-integer footstep planning for a walking robot
Deits, Robin L. H. (Robin Lloyd Henderson)
2014-01-01
This work presents a novel formulation of the footstep planning problem as a mixed-integer convex optimization. The footstep planning problem involves choosing a set of footstep locations which a walking robot can follow ...
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants
NASA Astrophysics Data System (ADS)
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-01
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient’s anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant’s RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B1+ field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient’s anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants.
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-21
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient's anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant's RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the [Formula: see text] field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient's anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty. PMID:26350025
Abbeel, Pieter
, bevel-tip medical needles, planning curvature-constrained channels in 3D printed implants for targeted in 3D environments. We report two main contributions in this work: (i) curvature-constrained trajectory for perturbations. Our ap- proach can also be used for designing optimized channel layouts within 3D printed
Constructing Approximations to the Efficient Set of Convex Quadratic Multiobjective Problems
Fliege, Jörg
], and scheduling [3, 31]), environmental analysis [28, * *16, 18], cancer treatment planning [25], etc. Usually objective function value. However, this optimality definition is not as sim* *ple as the one from to gain as * *much information as possible about the solution set of a given problem, preferably
Applying optimization software libraries to engineering problems
NASA Technical Reports Server (NTRS)
Healy, M. J.
1984-01-01
Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.
Convex Nondifferentiable Optimization: a Survey Focussed on the Analytic Center Cutting Plane Method
J.-L. Goffin; JEAN-PHILIPPE VIAL
1999-01-01
We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant fucntions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis
Exploiting Problem Structure for Distributed Constraint Optimization
Jyi-shane Liu; Katia P. Sycara
1995-01-01
Distributed constraint optimization imposes considerabl e complexity in agents' coordinated search for an optimal so- lution. However, in many application domains, problems often exhibit special structures that can be exploited to fa - cilitate more efficient problem solving. One of the most recurrent structures involves disparity among subproblem s. We present a coordination mechanism, Anchor&Ascend, for distributed constraint optimization that
Convergence properties of minimization for convex constraints
Toint, Philippe
the structured trust region mechanism, we prove global convergence for all algorithms in our class. 1Convergence properties of minimization algorithms for convex constraints using a structured trust.48.4.14) Keywords : Trust region methods, structured problems, largescale optimization, partial sepa rability
Models for optimal harvest with convex function of growth rate of a population
Lyashenko, O.I.
1995-12-10
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.
Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems
NASA Astrophysics Data System (ADS)
Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao
Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.
NASA Astrophysics Data System (ADS)
Liolios, K.; Georgiev, I.; Liolios, A.
2012-10-01
A numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soil-pipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the non-convex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and a non-convex linear complementarity problem is solved in each time-step.
Towards Optimal Techniques for Solving Global Optimization Problems
Kreinovich, Vladik
at El Paso, El Paso, TX 79968, USA vladik@utep.edu 1 Introduction 1.1 Global OptimizationTowards Optimal Techniques for Solving Global Optimization Problems: SymmetryBased Approach, Princeton, NJ 08544, USA floudas@titan.princeton.edu 2 Department of Computer Science, University of Texas
Towards Optimal Techniques for Solving Global Optimization Problems
Kreinovich, Vladik
at El Paso, El Paso, TX 79968, USA vladik@utep.edu 1 Introduction 1.1 Global Optimization an ImportantTowards Optimal Techniques for Solving Global Optimization Problems: Symmetry-Based Approach, Princeton, NJ 08544, USA floudas@titan.princeton.edu 2 Department of Computer Science, University of Texas
GLOBAL OPTIMIZATION FOR THE PHASE STABILITY PROBLEM
Neumaier, Arnold
GLOBAL OPTIMIZATION FOR THE PHASE STABILITY PROBLEM Conor M. McDonald and Christodoulos A. Floudas equations. It is shown how the global minimum of the tangent plane distance function can be obtained for this class of problems. The advantage of a global optimization approach is that if a nonnegative solution
W. C. Stirling; D. R. Morrell
1991-01-01
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
Willsky, Alan S.
, these additional constraints arise in problems involving attitude estimation for spacecraft [27], pose estimation such as spacecraft or molecules. The set of n × n rotation matrices is non-convex, so optimization problems over attitude and spin-rate of a spinning satellite and show how to reformulate this ostensibly non- convex
Problem Solving through an Optimization Problem in Geometry
ERIC Educational Resources Information Center
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
Representations in Problem Solving: A Case Study with Optimization Problems
ERIC Educational Resources Information Center
Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose
2009-01-01
Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…
Hybrid unicast and multicast flow control: A linear optimization approach
Yousefi'zadeh, H; Fazel, F; Jafarkhani, H
2004-01-01
and Multicast Flow Control: A Linear Optimization Approachcontrol problem is now described in the form of the following Linearcontrol problem is a convex optimization problem de? ned over a set of piecewise linear
Optimization problems in network connectivity
Panigrahi, Debmalya
2012-01-01
Besides being one of the principal driving forces behind research in algorithmic theory for more than five decades, network optimization has assumed increased significance in recent times with the advent and widespread use ...
Convex Formulations of Learning from Crowds
NASA Astrophysics Data System (ADS)
Kajino, Hiroshi; Kashima, Hisashi
It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.
Hybrid intelligent optimization methods for engineering problems
Yasin Volkan Pehlivanoglu
2010-01-01
The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients
Exploiting phase transitions for fusion optimization problems
NASA Astrophysics Data System (ADS)
Svenson, Pontus
2005-05-01
Many optimization problems that arise in multi-target tracking and fusion applications are known to be NP-complete, ie, believed to have worst-case complexities that are exponential in problem size. Recently, many such NP-complete problems have been shown to display threshold phenomena: it is possible to define a parameter such that the probability of a random problem instance having a solution jumps from 1 to 0 at a specific value of the parameter. It is also found that the amount of resources needed to solve the problem instance peaks at the transition point. Among the problems found to display this behavior are graph coloring (aka clustering, relevant for multi-target tracking), satisfiability (which occurs in resource allocation and planning problem), and the travelling salesperson problem. Physicists studying these problems have found intriguing similarities to phase transitions in spin models of statistical mechanics. Many methods previously used to analyze spin glasses have been used to explain some of the properties of the behavior at the transition point. It turns out that the transition happens because the fitness landscape of the problem changes as the parameter is varied. Some algorithms have been introduced that exploit this knowledge of the structure of the fitness landscape. In this paper, we review some of the experimental and theoretical work on threshold phenomena in optimization problems and indicate how optimization problems from tracking and sensor resource allocation could be analyzed using these results.
Patriksson, Michael
.1 Motivation Topology optimization of mechanical structures refers to the subfield of structural optimizationExistence and continuity of optimal solutions to some structural topology optimization problems April 25, 2000 Abstract We consider a general discrete structural optimization problem including
Belief Propagation Algorithm for Portfolio Optimization Problems
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462
Optimization Problems in Wireless Sensor Networks
Ada Gogu; Dritan Nace; Arta Dilo; Nirvana Meratnia
2011-01-01
The Wireless Sensor Networks (WSNs) design related questions give rise to new complex and difficult the- oretical problems and challenges in operations research and optimization areas. As WSNs become increasingly pervasive, a good understanding of these problems in terms of theoretical complexity is of great help in designing appropriate algorithms. In this paper, we examine some of the most fundamental
Bach, Francis
of homogenous subsets of data. Algorithms such as k-means, Gaussian mixture models, hierarchical clustering experimentally gives state-of- the-art results similar to spectral clustering for non-convex clusters, and has from instabilities, either because they are cast as non- convex optimization problems, or because
A Convex Guidance Algorithm for Formation Reconfiguration
NASA Technical Reports Server (NTRS)
Acikmese, A. Behcet; Schar, Daniel P.; Murray, Emmanuell A.; Hadaeghs, Fred Y.
2006-01-01
In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.
Constructing Dynamic Optimization Test Problems Using the Multi-objective
Jin, Yaochu
-objective optimization (MOO) concepts. By aggregating different objectives of an MOO problem and changing the weights-objective optimization and thus the rich MOO test problems can easily be adapted to dynamic optimization test functions
Rotkowitz, Michael C.
the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing that the controllers to be designed all have access to the same measurements. With the advent of complex systems automobiles on the freeway, the power distribution grid, spacecraft moving in formation, and paper machining
Lisbon, University of
Shape and Topology Optimization for Periodic Problems Part II: Optimization algorithm and numerical which alternates shape and topology optimization (the theoretical background about shape and topological Regeneration Â· Shape Optimization Â· Topology Optimization Â· Auxetic Materials 1 Introduction The main
NASA Astrophysics Data System (ADS)
Dudek, Sylwia; Kalita, Piotr; Migórski, Stanis?aw
2015-07-01
In this paper, we study the steady-state (coupled) conduction-radiation heat transfer phenomenon in a non-convex opaque blackbody with temperature-dependent thermal conductivity. The mathematical description consists of a nonlinear partial differential equation subjected to a nonlinear boundary condition involving an integral operator that is inherently associated with the non-convexity of the body. The unknown is the absolute temperature distribution. The problem is rewritten with the aid of a Kirchhoff transformation, giving rise to linear partial differential equation and a new unknown. An iterative procedure is proposed for constructing the solution of the problem by means of a sequence of problems, each of them with an equivalent minimum principle. Proofs of convergence as well as existence and uniqueness of the solution are presented. An error estimate, for each element of the sequence, is presented too.
Solving optimization problems on computational grids.
Wright, S. J.; Mathematics and Computer Science
2001-05-01
Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms have become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software infrastructure need to solve these problems on computational grids. This article describes some of the results we have obtained during the first three years of the metaneos project. Our efforts have led to development of the runtime support library MW for implementing algorithms with master-worker control structure on Condor platforms. This work is discussed here, along with work on algorithms and codes for integer linear programming, the quadratic assignment problem, and stochastic linear programmming. Our experiences in the metaneos project have shown that cheap, powerful computational grids can be used to tackle large optimization problems of various types. In an industrial or commercial setting, the results demonstrate that one may not have to buy powerful computational servers to solve many of the large problems arising in areas such as scheduling, portfolio optimization, or logistics; the idle time on employee workstations (or, at worst, an investment in a modest cluster of PCs) may do the job. For the optimization research community, our results motivate further work on parallel, grid-enabled algorithms for solving very large problems of other types. The fact that very large problems can be solved cheaply allows researchers to better understand issues of 'practical' complexity and of the role of heuristics.
Statistical physics of hard optimization problems
NASA Astrophysics Data System (ADS)
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
Exact Matrix Completion via Convex Optimization Emmanuel J. Cand`es
Qiu, Robert Caiming
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
MANUSCRIPT SUBMITTED TO IEEE TRANS. PAMI, AUGUST 2011. 1 Convex Optimization Based Low-Rank Matrix
Ma, Yi
Completion and Recovery for Photometric Stereo and Factor Classification Lun Wu, Student Member, IEEE, Arvind the photometric stereo problem. We cast the problem of recovering surface normals from images taken under multiple and specularities. The new technique can be used to improve virtually any existing photometric stereo method. We
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. PMID:24832358
Wang, Yong; Li, Han-Xiong; Yen, Gary G; Song, Wu
2015-04-01
In the field of evolutionary computation, there has been a growing interest in applying evolutionary algorithms to solve multimodal optimization problems (MMOPs). Due to the fact that an MMOP involves multiple optimal solutions, many niching methods have been suggested and incorporated into evolutionary algorithms for locating such optimal solutions in a single run. In this paper, we propose a novel transformation technique based on multiobjective optimization for MMOPs, called MOMMOP. MOMMOP transforms an MMOP into a multiobjective optimization problem with two conflicting objectives. After the above transformation, all the optimal solutions of an MMOP become the Pareto optimal solutions of the transformed problem. Thus, multiobjective evolutionary algorithms can be readily applied to find a set of representative Pareto optimal solutions of the transformed problem, and as a result, multiple optimal solutions of the original MMOP could also be simultaneously located in a single run. In principle, MOMMOP is an implicit niching method. In this paper, we also discuss two issues in MOMMOP and introduce two new comparison criteria. MOMMOP has been used to solve 20 multimodal benchmark test functions, after combining with nondominated sorting and differential evolution. Systematic experiments have indicated that MOMMOP outperforms a number of methods for multimodal optimization, including four recent methods at the 2013 IEEE Congress on Evolutionary Computation, four state-of-the-art single-objective optimization based methods, and two well-known multiobjective optimization based approaches. PMID:25099966
Evolutionary optimality in stochastic search problems.
Preston, Mark D; Pitchford, Jonathan W; Wood, A Jamie
2010-09-01
'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
Optimal solutions of unobservable orbit determination problems
NASA Astrophysics Data System (ADS)
Cicci, David A.; Tapley, Byron D.
1988-12-01
The method of data augmentation, in the form ofa priori covariance information on the reference solution, as a means to overcome the effects of ill-conditioning in orbit determination problems has been investigated. Specifically, for the case when ill-conditioning results from parameter non-observability and an appropriatea priori covariance is unknown, methods by which thea priori covariance is optimally chosen are presented. In problems where an inaccuratea priori covariance is provided, the optimal weighting of this data set is obtained. The feasibility of these ‘ridge-type’ solution methods is demonstrated by their application to a non-observable gravity field recovery simulation. In the simulation, both ‘ridge-type’ and conventional solutions are compared. Substantial improvement in the accuracy of the conventional solution is realized by the use of these ridge-type solution methods. The solution techniques presented in this study are applicable to observable, but ill-conditioned problems as well as the unobservable problems directly addressed. For the case of observable problems, the ridge-type solutions provide an improvement in the accuracy of the ordinary least squares solutions.
10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method
Tibshirani, Ryan
rule converges to the square root of S, which turns out to be a special case of Newton method.1 Motivation Newton method is originally developed for finding a root of a function. It is also known as Newton first applied the Newton method to find the square root of a positive number S R+. The problem can
LDRD Final Report: Global Optimization for Engineering Science Problems
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
Numerical Approximations of Stochastic Optimal Stopping and Control Problems
Siska, David
2007-01-01
We study numerical approximations for the payoff function of the stochastic optimal stopping and control problem. It is known that the payoff function of the optimal stopping and control problem corresponds to the solution ...
Inverse Optimization: An Application to the Capacitated Plant Location Problem
Bitran, Gabriel R.
Inverse optimization refers to the fact that each time a Lagrangean derived from a given mathematical programming problem is solved, it produces an optimal solution to some problem with a different right hand side. This ...
Convex Optimization for the Design of Learning K. Pelckmans, J.A.K. Suykens, B. De Moor
which can be written as min x f0(x) s.t. fk(x) = 0 k = 1, . . . , nK fl(x) 0 l = nK + 1, . . . , nK + n for all k = 1, . . . , nK are linear in terms of x, and the inequality constraints fl : Rv R for all l = nK + 1, . . . , nK + nL are convex ([11], Sect 4.2). Among the principal advantages of such convex
Honey Bees Mating Optimization for the location routing problem
Yannis Marinakis; Magdalene Marinaki; Nikolaos Matsatsinis
2008-01-01
This paper introduces a new hybrid algorithmic nature inspired approach based on honey bees mating optimization, for solving successfully one of the most popular supply chain management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid honey bees mating optimization (HBMO-LRP), combines a honey bees mating optimization (HBMO) algorithm, the
A COMPUTATIONAL ANALYSIS OF THE OPTIMAL POWER FLOW PROBLEM
A COMPUTATIONAL ANALYSIS OF THE OPTIMAL POWER FLOW PROBLEM By Baha Alzalg, CatalinA Anghel, Wenying ANALYSIS OF THE OPTIMAL POWER FLOW PROBLEM BAHA ALZALG, CATALINA ANGHEL, WENYING GAN, QING HUANG, MUSTAZEE RAHMAN, AND ALEX SHUM Abstract. The optimal power flow problem is concerned with finding a proper
Optimal Planning and Problem-Solving
NASA Technical Reports Server (NTRS)
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
Optimal Stopping of Markov chain, Gittins Index and Related Optimization Problems
Sonin, Isaac
Optimal Stopping of Markov chain, Gittins Index and Related Optimization Problems Isaac M. Sonin in Google New York, Columbia University, September 2011 Isaac M. Sonin Optimal Stopping of Markov chain, Gittins Index and Related Optimization Problems New York, Columbia University, / 25 #12;Outline Optimal
IEEE INFOCOM 2002 1 QoS and Fairness Constrained Convex
IEEE INFOCOM 2002 1 QoS and Fairness Constrained Convex Optimization of Resource Allocation-- For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations- date a variety of realistic QoS and fairness constraints. Their glob- ally optimal solutions can
Fast Approximate Convex Decomposition
Ghosh, Mukulika
2012-10-19
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...
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.
Optimal Auction Design for Agents with Hard Valuation Problems
Chen, Yiling
Optimal Auction Design for Agents with Hard Valuation Problems David C. Parkes ? Computer human expert. Although auction design cannot simplify the valuation problem itself, we show that good. Keywords: agent-mediated electronic commerce, valuation problem, metade- liberation, auction theory
Semard, Gaëlle; Peulon-Agasse, Valerie; Bruchet, Auguste; Bouillon, Jean-Philippe; Cardinaël, Pascal
2010-08-13
It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater. PMID:20633886
Minimax optimization problem of structural design Elena Cherkaev *, Andrej Cherkaev
Cherkaev, Andrej
Minimax optimization problem of structural design Elena Cherkaev *, Andrej Cherkaev University discusses a problem of robust optimal design of elastic structures when the loading is unknown design should optimize the behavior of the structure in the worst possible scenario, which itself depends
Optimal Stopping Problems for Time-Homogeneous Diffusions: a Review
Pedersen, Jesper Lund
Optimal Stopping Problems for Time-Homogeneous Diffusions: a Review Jesper Lund Pedersen ETH, ZÂ¨urich The first part of this paper summarises the essential facts on general optimal stopping theory for time for the value function and the optimal stopping boundary as a free-boundary (Stefan) problem and further
Optimal shape design as a material distribution problem
M. P. Bendsøe
1989-01-01
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
Aerodynamic Shape Optimization of Benchmark Problems Using Jetstream
Zingg, David W.
and the rise of jet fuel prices pressure aircraft manufacturers to prioritize minimizing fuel burn when supplied to a sequential quadratic programming optimization algorithm. The first optimization problem to the Discussion Group problem suite. The first is a wing-fuselage-tail optimization with a prescribed spanwise
Patriksson, Michael
Introduction 1.1 Motivation Topology optimization of mechanical structures refers to the subfield of structuralExistence and continuity of optimal solutions to some structural topology optimization problems September 26, 2001 Abstract We consider a general discrete structural optimization problem including
An Optimal Control Problem in Medical Image Processing
Kristian Bredies; Dirk A. Lorenz; P. Maass
2006-01-01
As a starting point of this paper we present a problem from mam- mographic image processing. We show how it can be formulated as an optimal control problem for PDEs and illustrate that it leads to penalty terms which are non-standard in the theory of optimal control of PDEs. To solve this control problem we use a generalization of the
Chan, Carri W
2008-01-01
This paper presents a general class of dynamic stochastic optimization problems we refer to as Stochastic Depletion Problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as also from a theoretical perspective. As such, simple heuristics are highly desirable. We isolate two simple properties that, if satisfied by a problem within this class, guarantee that a myopic policy incurs a performance loss of at most 50 % relative to the optimal adaptive control policy for that problem. We are able to verify that these two properties are satisfied for several interesting families of stochastic depletion problems and as a consequence identify efficient near-optimal control policies for a number of interesting dynamic stochastic optimization problems.
Prophet inequalities for finite stage multiparameter optimal stopping problems
NASA Astrophysics Data System (ADS)
Tanaka, Teruo
2006-10-01
This paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set Nd. In the classical optimal stopping problems, the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet inequalities, have been studied by many authors. Prophet inequalities in the case of finite stage two-parameter optimal stopping problems are extended to the case of finite stage general multiparameter optimal stopping problems.
Progress in design optimization using evolutionary algorithms for aerodynamic problems
NASA Astrophysics Data System (ADS)
Lian, Yongsheng; Oyama, Akira; Liou, Meng-Sing
2010-07-01
Evolutionary algorithms (EAs) are useful tools in design optimization. Due to their simplicity, ease of use, and suitability for multi-objective design optimization problems, EAs have been applied to design optimization problems from various areas. In this paper we review the recent progress in design optimization using evolutionary algorithms to solve real-world aerodynamic problems. Examples are given in the design of turbo pump, compressor, and micro-air vehicles. The paper covers the following topics that are deemed important to solve a large optimization problem from a practical viewpoint: (1) hybridized approaches to speed up the convergence rate of EAs; (2) the use of surrogate model to reduce the computational cost stemmed from EAs; (3) reliability based design optimization using EAs; and (4) data mining of Pareto-optimal solutions.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
An exact solution to the transistor sizing problem for CMOS circuits using convex optimization
Sachin S. Sapatnekar; Vasant B. Rao; Pravin M. Vaidya; Sung-mo Kang
1993-01-01
Abstract: this paper.Given the MOS circuit topology, the delay can be controlled byvarying the sizesof transistors in the circuit. Here, the size of a transistor is measured in terms of its channelwidth, since the channel lengths in a digital circuit are generally uniform. Roughly speaking,the sizes of certain transistors can be increased to reduce the circuit delay at the expense
A Note on Irreversible Investment, Hedging and Optimal Consumption Problems
A Note on Irreversible Investment, Hedging and Optimal Consumption Problems Vicky Henderson and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic of determining the optimal timing of an irreversible investment decision in an incomplete market, for an agent
The Role of Intuition in the Solving of Optimization Problems
ERIC Educational Resources Information Center
Malaspina, Uldarico; Font, Vicenc
2010-01-01
This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…
Combinatorial optimization problems with normal random costs Paolo Serafini
Serafini, Paolo
, Department of Mathematics and Computer Science Abstract. We consider combinatorial optimization problems the following general definition of a combinatorial optimization problem: a finite set E and a family X according to this definition. In this paper we consider the extension of the previous definition to the case
GimÃ©nez, Domingo
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
Graph Implementations for Nonsmooth Convex Programs
programming, conic optimization, nondifferentiable functions. 1 Introduction It is well known that convex, as well as for certain standard forms such as semidefinite programs (SDPs), that are efficient in bothGraph Implementations for Nonsmooth Convex Programs Michael C. Grant I and Stephen P. Boyd 2 1
Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems
NASA Technical Reports Server (NTRS)
Balling, R. J.; Wilkinson, C. A.
1997-01-01
A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.
Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution
Longin Jan Latecki; Rolf Lakämper
1999-01-01
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
Robust stability and contraction analysis of nonlinear systems via semidefinite optimization
Aylward, Erin M
2006-01-01
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 ...
Use of Regularization Functions in Problems of Dynamic Optimization
Grossmann, Ignacio E.
Functions in Problems of Dynamic Optimization 7 Numerical Applications 1. Condenser-Tank - Pantelides(1988 in Problems of Dynamic Optimization 8 Switching between models allowing continuous integration of the problem , with 0 0 , , with 0 1 where : 1 with and 0 final u t s p s p te f P t S S P P K S K dx S P x x g Sdt S P
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
Stochastic Analyses for Online Combinatorial Optimization Problems
Gupta, Anupam
.1) where r is the set of random coins flipped by the algorithm, the maximum is taken over all inputs and clean problems, and strong upper and lower bounds on the competitive ratio are known for most problems
Linear Reformulation of Probabilistically Constrained Optimization Problems
probability distribution with finite support Approach: Combinatorial pattern approach Rationale: Capturing) Pollution (Gren, 2008) Production-distribution problems (LE, Ruszczy´nski, 2007) Munitions prepositioning;Solution Methods p-efficiency concept (Prékopa, 1990): disjunctive problem: Identification of finite
A Hierarchical Particle Swarm Optimizer for Dynamic Optimization Problems
Stefan Janson; Martin Middendorf
2004-01-01
\\u000a Particle Swarm Optimization (PSO) methods for dynamic function optimization are studied in this paper. We compare dynamic\\u000a variants of standard PSO and Hierarchical PSO (H-PSO) on different dynamic benchmark functions. Moreover, a new type of hierarchical\\u000a PSO, called Partitioned H-PSO (PH-PSO), is proposed. In this algorithm the hierarchy is partitioned into several sub-swarms\\u000a for a limited number of generations after
Some global optimization problems on Stiefel manifolds ?
Csendes, Tibor
, Hungary T. Csendes Institute of Informatics, University of Szeged, H-6701 Szeged, POB 652, Hungary T, Hungarian Academy of Sciences, H-1518 Budapest, POB 63, Hungary Abstract Optimization on Stiefel manifolds
A Planning Problem Combining Calculus of Variations and Optimal Transport
Carlier, G., E-mail: carlier@ceremade.dauphine.fr; Lachapelle, A., E-mail: lachapelle@ceremade.dauphine.f [Universite Paris IX Dauphine, CEREMADE, UMR CNRS 7534 (France)
2011-02-15
We consider some variants of the classical optimal transport where not only one optimizes over couplings between some variables x and y but also over some control variables governing the evolutions of these variables with time. Such a situation is motivated by an assignment problem of tasks with workers whose characteristics can evolve with time (and be controlled). We distinguish between the coupled and decoupled case. The coupled case is a standard optimal transport with the value of some optimal control problem as cost. The decoupled case is more involved since it is nonlinear in the transport plan.
Multiple local minima in radiotherapy optimization problems with dose-volume constraints.
Deasy, J O
1997-07-01
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
Comparison of optimal design methods in inverse problems
NASA Astrophysics Data System (ADS)
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Heermann, Dieter W.
a local cost si(x), while the regularizer J enforces the desired spatial coherency. In terms of Markov the desired optimality, and provides -optimal solutions in O(1/). 1.2. Related Work The continuous two
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
Approximate Solutions to Several Visibility Optimization Problems
Ferguson, Thomas S.
on the route. These problems are similar to the art gallery and watchman route problems, respectively. We propose a greedy iterative algorithm, formulated in the level set framework as the solution to the art that divides a domain () pop- ulated with occluders into visible and invisible regions as observed from
Direct Multiple Shooting Optimization with Variable Problem Parameters
NASA Technical Reports Server (NTRS)
Whitley, Ryan J.; Ocampo, Cesar A.
2009-01-01
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Some Optimal Stochastic Control Problems in Neuroscience — a Review
NASA Astrophysics Data System (ADS)
Feng, Jianfeng; Chen, Xiaojiang; Tuckwell, Henry C.; Vasilaki, Eleni
Nervous systems are probability machines and, as such, modeling their activities should incorporate stochastic processes. In this review, we present two examples of optimal stochastic control problems with an analytic methodology on how to find optimal signals. The first example deals with neuronal activity and the second example is concerned with a higher level task: arm movement. In both cases we find optimal signals for particular tasks and find our results in agreement with the experimental Fitts Law.
Dominance rules in combinatorial optimization problems Antoine Jouglet & Jacques Carlier
Paris-Sud XI, Université de
Dominance rules in combinatorial optimization problems Antoine Jouglet & Jacques Carlier UMR CNRS is to study the concept of a "dominance rule" in the context of combi- natorial optimization. A dominance rule. Dominance rules have been extensively used over the last fifty years. Surprisingly, to our knowledge
Optimal demand response: problem formulation and deterministic case
Low, Steven H.
Optimal demand response: problem formulation and deterministic case Lijun Chen, Na Li, Libin Jiang load through real-time demand response and purchases balancing power on the spot market to meet, optimal demand response reduces to joint scheduling of the procurement and consumption decisions
Some Finance Problems Solved with Nonsmooth Optimization Techniques
Vinter, Richard
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
On VEPSO and VEDE for Solving a Treaty Optimization Problem
Rau-Chaplin, Andrew
Evaluated Particle Swarm Optimization (VEPSO) in solv- ing a real world financial optimization problem in computational finance, and their performance has been evaluated in terms of metrics including the average number used; Section IV presents metrics, parameters and the perfor- mance evaluation; finally, Section V
A Decision Support System for Solving Multiple Criteria Optimization Problems
ERIC Educational Resources Information Center
Filatovas, Ernestas; Kurasova, Olga
2011-01-01
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
Optimal Policies for a Multi-Echelon Inventory Problem
Andrew J. Clark; Herbert Scarf
1960-01-01
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
Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems
Papalambros, Panos
Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems Zhoujie Lyu Aerodynamic shape optimization based on high-fidelity models is a computational intensive endeavor. The techniques are tested using the Common Research Model wing benchmark defined by the Aerodynamic Design
Numerical solution of optimal control problems for complex power systems
NASA Astrophysics Data System (ADS)
Kalimoldayev, Maksat N.; Jenaliyev, Muvasharkhan T.; Abdildayeva, Asel A.; Elezhanova, Shynar K.
2015-09-01
The questions about the decision of optimal control problems for nonlinear system of ordinary differential equations have been considered in this work. In particular, the model considered in this paper describes the controlled processes in electric power systems. Proposed solution methods follow up the principle of expansion of extreme problems based on V.F. Krotov's sufficient conditions of optimality. Numerical experiments shows sufficient efficiency of the used algorithm.
Combinatorial optimization problems with concave costs
Stratila, Dan
2009-01-01
In the first part, we study the problem of minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can ...
introduction first problem two optimization problems in physiology
Combettes, Patrick Louis
first problem FDG-PET FDG is a glucose analog that allows tracking glucose metabolism glucose on the aggressiveness of cells the amount of FDG at disposal in the environment co-morbidities: what if cancer: homogeneous functional behavior (focused on tracer metabolism) input for kinetics: FDG concentration in blood
Josi?ski, Henryk; Michalczuk, Agnieszka; ?wito?ski, Adam
2014-01-01
This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420
Chapter 4: Unconstrained Optimization Unconstrained optimization problem minx F(x) or maxx F(x)
Wu, Xiaolin
Chapter 4: Unconstrained Optimization Â· Unconstrained optimization problem minx F(x) or maxx F(x) Â· Constrained optimization problem min x F(x) or max x F(x) subject to g(x) = 0 and/or h(x) 0 Example: minimize the outer area of a cylinder subject to a fixed volume. Objective function F(x) = 2r2
Josi?ski, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Swito?ski, Adam
2014-01-01
This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420
Exact solution for an optimal impermeable parachute problem
NASA Astrophysics Data System (ADS)
Lupu, Mircea; Scheiber, Ernest
2002-10-01
In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.
Fundamental differences between optimization code test problems in engineering applications
NASA Technical Reports Server (NTRS)
Eason, E. D.
1984-01-01
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.
Optimal boundary control problems related to high-lift configurations
Tröltzsch, Fredi
optimal boundary control problem for the two- dimensional Navier-Stokes equations with low Reynolds number problems related to the aerodynamic optimiza- tion of flows around airfoils in high-lift configurations the flow around airfoils. The associated background of applications in fluid mechanics, active separation
SIMULATION OPTIMIZATION OF THE CROSSDOCK DOOR ASSIGNMENT PROBLEM
Aickelin, Uwe
SIMULATION OPTIMIZATION OF THE CROSSDOCK DOOR ASSIGNMENT PROBLEM Dr. Uwe Aickelin Adrian Adewunmi of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment
Finding Globally Optimum Solutions in Antenna Optimization Problems
Hajimiri, Ali
as the optimization variables. This is particularly useful in designing on-chip smart antennas, where thousands in designing smart antennas. Description of the Problem Let us consider the problem in Figure 1, where a dipole. Unfortunately, in this case, the total number of possibilities increases exponentially with the number of metal
The Traveling Salesman Problem: A Case Study in Local Optimization
Hutter, Frank
The Traveling Salesman Problem: A Case Study in Local Optimization David S. Johnson1 Lyle A. Mc i, j N. The symmetric traveling salesman problem has many applications, from VLSI chip fabrication Lawler, Lenstra, Rinnooy Kan, and Shmoys [1985]. It is NP- hard [Garey & Johnson, 1979] and so any
An optimal replacement problem in aluminum production
Spanks, Lisa Marie
1992-01-01
that there are three possible maintenance decisions: 1) replace the pot, 2) minimally repair the pot, or 3) leave the pot alone. The objective of this research is to develop a procedure, using a finite planning horizon, to determine the maintenance policy...'s aluminum production facility in Rockdale, Texas. The optimal policy consists of the unique and finite pot ages to and t*; where if a failure occurs during the interval [O, t ), a minimal repair is the action taken; and if a failure occurs during...
Cooperative optimal path planning for herding problems
Lu, Zhenyu
2009-05-15
of as a shepherd and the evader as a member of a ock. A. System Model x r Pursuer ? Evader y [0,0] ? Fig. 1. System Model for 1P1E Figure 1 gives us a representation of the two agents. The pursuer is generally located at [xp,yp] and the evader... is generally located at [xe,ye]. Beginning at the 5 initial positions, [xp0,yp0] for the pursuer and [xe0,ye0] for the evader, the pursuer should optimally drive the evader to a certain location or region. For the 1P1E scenario, this is the [0,0] position...
Combinatorial Patterns for Probabilistically Constrained Optimization Problems
b P hj (x) j, j J p x R+ × Z+ with having a multivariate probability distribution with finite (Prékopa, 1990): disjunctive problem: Identification of finite, unknown number of p-efficient points of the discrete probability distribution F if: F(v) p , and there is no v v, v = v such that F(v ) p
Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian
2013-01-01
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
Nonlinear singularly perturbed optimal control problems with singular arcs
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1977-01-01
A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.
Branch and Bound Methods for Euclidean Registration Problems
Lunds Universitet
for camera pose, may get trapped in local minima due to the non-convexity of the corresponding optimization to the local minima problem. Index Terms-- Registration, camera pose, global optimization, branch and bound. I. A related problem is the camera pose problem, that is, finding the perspective mapping between an object
Convex-relaxed kernel mapping for image segmentation.
Ben Salah, Mohamed; Ben Ayed, Ismail; Jing Yuan; Hong Zhang
2014-03-01
This paper investigates a convex-relaxed kernel mapping formulation of image segmentation. We optimize, under some partition constraints, a functional containing two characteristic terms: 1) a data term, which maps the observation space to a higher (possibly infinite) dimensional feature space via a kernel function, thereby evaluating nonlinear distances between the observations and segments parameters and 2) a total-variation term, which favors smooth segment surfaces (or boundaries). The algorithm iterates two steps: 1) a convex-relaxation optimization with respect to the segments by solving an equivalent constrained problem via the augmented Lagrange multiplier method and 2) a convergent fixed-point optimization with respect to the segments parameters. The proposed algorithm can bear with a variety of image types without the need for complex and application-specific statistical modeling, while having the computational benefits of convex relaxation. Our solution is amenable to parallelized implementations on graphics processing units (GPUs) and extends easily to high dimensions. We evaluated the proposed algorithm with several sets of comprehensive experiments and comparisons, including: 1) computational evaluations over 3D medical-imaging examples and high-resolution large-size color photographs, which demonstrate that a parallelized implementation of the proposed method run on a GPU can bring a significant speed-up and 2) accuracy evaluations against five state-of-the-art methods over the Berkeley color-image database and a multimodel synthetic data set, which demonstrates competitive performances of the algorithm. PMID:24723519
Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.
2000-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.
Integrated network design and scheduling problems : optimization algorithms and applications.
Nurre, Sarah G.; Carlson, Jeffrey J.
2014-01-01
We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.
Buchanan, Catherine
2008-01-01
The primary focus of this work is a thorough research into the current available techniques for solving nonlinear programming problems. Emphasis is placed on interior-point methods and the connection between optimal ...
Convex Models of Distribution System Reconfiguration
Taylor, Joshua A.
We derive new mixed-integer quadratic, quadratically constrained, and second-order cone programming models of distribution system reconfiguration, which are to date the first formulations of the ac problem that have convex, ...
Climate Intervention as an Optimization Problem
NASA Astrophysics Data System (ADS)
Caldeira, Ken; Ban-Weiss, George A.
2010-05-01
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.
Convex sets Let , , the through
Ferland, Jacques A.
Convex sets Non convex sets ( ),x y x y Â· Â· Â· Â· x y #12;y ( ){ } ( ) ( ) 1 Let , , the through x y X Convex sets Non convex sets ( ),x y x y Â· Â· Â· Â· #12;y ( ){ } ( ) ( ) 1 Let x y X Convex sets Non convex sets ( ),x y x y Â· Â· Â· Â· #12;Recall: Notation et definitions
It looks easy! Heuristics for combinatorial optimization problems.
Chronicle, Edward P; MacGregor, James N; Ormerod, Thomas C; Burr, Alistair
2006-04-01
Human performance on instances of computationally intractable optimization problems, such as the travelling salesperson problem (TSP), can be excellent. We have proposed a boundary-following heuristic to account for this finding. We report three experiments with TSPs where the capacity to employ this heuristic was varied. In Experiment 1, participants free to use the heuristic produced solutions significantly closer to optimal than did those prevented from doing so. Experiments 2 and 3 together replicated this finding in larger problems and demonstrated that a potential confound had no effect. In all three experiments, performance was closely matched by a boundary-following model. The results implicate global rather than purely local processes. Humans may have access to simple, perceptually based, heuristics that are suited to some combinatorial optimization tasks. PMID:16707362
Application of tabu search to deterministic and stochastic optimization problems
NASA Astrophysics Data System (ADS)
Gurtuna, Ozgur
During the past two decades, advances in computer science and operations research have resulted in many new optimization methods for tackling complex decision-making problems. One such method, tabu search, forms the basis of this thesis. Tabu search is a very versatile optimization heuristic that can be used for solving many different types of optimization problems. Another research area, real options, has also gained considerable momentum during the last two decades. Real options analysis is emerging as a robust and powerful method for tackling decision-making problems under uncertainty. Although the theoretical foundations of real options are well-established and significant progress has been made in the theory side, applications are lagging behind. A strong emphasis on practical applications and a multidisciplinary approach form the basic rationale of this thesis. The fundamental concepts and ideas behind tabu search and real options are investigated in order to provide a concise overview of the theory supporting both of these two fields. This theoretical overview feeds into the design and development of algorithms that are used to solve three different problems. The first problem examined is a deterministic one: finding the optimal servicing tours that minimize energy and/or duration of missions for servicing satellites around Earth's orbit. Due to the nature of the space environment, this problem is modeled as a time-dependent, moving-target optimization problem. Two solution methods are developed: an exhaustive method for smaller problem instances, and a method based on tabu search for larger ones. The second and third problems are related to decision-making under uncertainty. In the second problem, tabu search and real options are investigated together within the context of a stochastic optimization problem: option valuation. By merging tabu search and Monte Carlo simulation, a new method for studying options, Tabu Search Monte Carlo (TSMC) method, is 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.
Ant colony optimization for solving university facility layout problem
NASA Astrophysics Data System (ADS)
Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin
2013-04-01
Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ? 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Numerical Solution of Some Types of Fractional Optimal Control Problems
Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.
2013-01-01
We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. PMID:24385874
Optimality problem of network topology in stocks market analysis
NASA Astrophysics Data System (ADS)
Djauhari, Maman Abdurachman; Gan, Siew Lee
2015-02-01
Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets' commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem
NASA Technical Reports Server (NTRS)
Naidu, D. S.; Hibey, J. L.; Charalambous, C.
1988-01-01
The optimal-control problem arising in coplanar orbital transfer using aeroassist technology is addressed. The maneuver involves the transfer from high earth orbit to low earth orbit with minimum fuel consumption. Simulations are carried out to obtain a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the present work is the application of an efficient multiple shooting method for handling the difficult nonlinear two-point boundary value problem resulting from the optimization procedure.
Vincenzo Lippiello; Bruno Siciliano; Luigi Villani
2011-01-01
The problem of grasping force optimization (GFO) for a multi-fingered robotic hand is considered in this paper. The GFO problem is cast in a convex optimization problem, considering also joint torque constraints. A new algorithmic solution is proposed here, which is suitable to be implemented online. The proposed formulation allows a substantial reduction of the computational load of the problem
Artificial bee colony algorithm for solving optimal power flow problem.
Le Dinh, Luong; Vo Ngoc, Dieu; Vasant, Pandian
2013-01-01
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
Artificial Bee Colony Algorithm for Solving Optimal Power Flow Problem
Le Dinh, Luong; Vo Ngoc, Dieu
2013-01-01
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
Binary optimization for source localization in the inverse problem of ECG.
Potyagaylo, Danila; Cortés, Elisenda Gil; Schulze, Walther H W; Dössel, Olaf
2014-09-01
The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance. PMID:25008005
Adapting Genetic Algorithms for Combinatorial Optimization Problems in Dynamic Environments
Abdunnaser Younes; Shawki Areibi; Paul Calamai; Otman Basir
2008-01-01
Combinatorial optimization problems (COPs) have a wide range of applications in engineering, operation research, and social sciences. Moreover, as real-time information and communication systems become increasingly available and the processing of real-time data becomes increasingly affordable, new versions of highly dynamic real-world applications are created. In such applications, information on the problem is not completely known a priori, but instead
NASA Astrophysics Data System (ADS)
Hassan, Md. Rakib; Islam, Md. Monirul; Murase, Kazuyuki
Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.
On optimality conditions for multiobjective optimization problems in topological vector space
NASA Astrophysics Data System (ADS)
Fulga, Cristinca; Preda, Vasile
2007-10-01
In this paper, we are concerned with a differentiable multiobjective programming problem in topological vector spaces. An alternative theorem for generalized K subconvexlike mappings is given. This permits the establishment of optimality conditions in this context: several generalized Fritz John conditions, in line to those in Hu and Ling [Y. Hu, C. Ling, The generalized optimality conditions of multiobjective programming problem in topological vector space, J. Math. Anal. Appl. 290 (2004) 363-372] are obtained and, in the presence of the generalized Slater's constraint qualification, the Karush-Kuhn-Tucker necessary optimality conditions.
Acuña, Daniel E.; Parada, Víctor
2010-01-01
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
Dominance Learning in Diploid Genetic Algorithms for Dynamic Optimization Problems
Yang, Shengxiang
Dominance Learning in Diploid Genetic Algorithms for Dynamic Optimization Problems Shengxiang Yang.yang@mcs.le.ac.uk ABSTRACT This paper proposes an adaptive dominance mechanism for diploidy genetic algorithms in dynamic environments. In this scheme, the genotype to phenotype mapping in each gene locus is controlled by a dominance
Optimizing Value and Avoiding Problems in Building Schools.
ERIC Educational Resources Information Center
Brevard County School Board, Cocoa, FL.
This report describes school design and construction delivery processes used by the School Board of Brevard County (Cocoa, Florida) that help optimize value, avoid problems, and eliminate the cost of maintaining a large facility staff. The project phases are examined from project definition through design to construction. Project delivery…
Optimal Website Design with the Constrained Subtree Selection Problem
Adler, Micah
Optimal Website Design with the Constrained Subtree Selection Problem Brent Heeringa1,2 and Micah of websites. Given a hierarchy of topics represented as a DAG G and a probability distribution over the topics design of websites given a set of page topics, weights for the topics, and a hierarchical arrangement
Cooperative ant colony optimization for multisatellite resource scheduling problem
Na Zhang; Zuren Feng
2007-01-01
Multisatellite resource scheduling problem is complicated and difficult to be solved because of the limited resources available. This paper develops a construction graph model of satellite overpasses, which involves several directed subgraphs. A cooperative ant colony optimization is employed to this model and to construct proper solutions, the ants in the same colony search in different subgraphs and communicate with
Multiagent Optimization System for Solving the Traveling Salesman Problem (TSP)
Xiao-Feng Xie; Jiming Liu
2009-01-01
The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP),
Optimization Problem Solving System using GridRPC
Dongarra, Jack
of multidisciplinary design op- timization and analysis such as automobile or aerospace design, several types the framework, end-users are able to design arbitrary applications integration through the wide area network the designed applications integration. These APIs support the creation of an optimization problem solving
To the optimization problem in minority game model
NASA Astrophysics Data System (ADS)
Yanishevsky, Vasyl
2009-12-01
The article presents the research results of the optimization problem in minority game model to a gaussian approximation using replica symmetry breaking by one step (1RSB). A comparison to replica symmetry approximation (RS) and the results from literary sources received using other methods has been held.
Simulation Optimization of the Crossdock Door Assignment Problem
Aickelin, Uwe
2008-01-01
The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.
Proposal of Evolutionary Simplex Method for Global Optimization Problem
NASA Astrophysics Data System (ADS)
Shimizu, Yoshiaki
To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.
A Convex Geometry-Based Blind Source Separation Method for Separating Nonnegative Sources.
Yang, Zuyuan; Xiang, Yong; Rong, Yue; Xie, Kan
2015-08-01
This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method. PMID:25203999
Optimizing investment fund allocation using vehicle routing problem framework
NASA Astrophysics Data System (ADS)
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method
NASA Astrophysics Data System (ADS)
Vasant, Pandian
2011-06-01
Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.
Particle Swarm Optimization and Its Applications in Power Systems
M. R. AlRashidi; M. F. AlHajri; A. K. Al-Othman; K. M. El-Naggar
\\u000a Optimization problems are widely encountered in various fields in science and technology. The fact that most optimization\\u000a problems, when modeled accurately, are of non-convex and sometimes discrete nature has encouraged many researchers to develop\\u000a new optimization techniques to overcome such difficulties. Particle Swarm Optimization (PSO) is one of the newly developed\\u000a optimization techniques with many attractive features. Early experimentations of
Optimal Stopping Rules For Some Blackjack Type Problems
NASA Astrophysics Data System (ADS)
Grzybowski, Andrzej Z.
2010-03-01
The paper deals with a class of optimal stopping problems having some features of blackjack type games. A decision maker observes sequentially the values of a finite sequence of non-negative random variables. After each observation he decides whether to stop or to continue. If he decides to stop, he obtains a payoff dependent on the sum of already observed values. The greater the sum, the more the decision maker gains, unless the sum exceeds a positive number T-a limit given in the problem. If so, the decision maker loses all or part of his payoff. A sufficient condition for existence of a simple optimal stopping rule for such problems is formulated. Then some special cases are considered in detail. Some numerical examples and practical questions are discussed as well.
A free boundary approach to shape optimization problems.
Bucur, D; Velichkov, B
2015-09-13
The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint. PMID:26261362
A robust Bayesian formulation of the optimal phase measurement problem
K. R. W. Jones
2012-12-15
Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an important test-bed for the development of robust statistical methods for instrument evaluation. However, the class of possible distributions exhibits extreme pathologies not commonly encountered in conventional statistical analysis. To overcome these difficulties we reformulate the basic variational problem of optimal phase measurement within a Bayesian paradigm and employ the Shannon information as a robust figure of merit. Single-mode performance bounds are discussed, and we invoke a general theorem that reduces the problem of finding the multi-mode performance bounds to the bounding of a single integral, without need of the central limit theorem.
Stanford University
Optimization Euclidean Distance Geometry 2 Moo Publishing #12;Meboo Publishing USA PO Box 12 Palo Alto, California 94302 Dattorro, Convex Optimization Euclidean Distance Geometry, second edition, Moo, v2015 but limited to personal use. 2005-2015 Moo Publishing USA #12;for Jennie Columba Antonio & Sze Wan #12;EDM
Block-oriented modeling of superstructure optimization problems
Friedman, Z; Ingalls, J; Siirola, JD; Watson, JP
2013-10-15
We present a novel software framework for modeling large-scale engineered systems as mathematical optimization problems. A key motivating feature in such systems is their hierarchical, highly structured topology. Existing mathematical optimization modeling environments do not facilitate the natural expression and manipulation of hierarchically structured systems. Rather, the modeler is forced to "flatten" the system description, hiding structure that may be exploited by solvers, and obfuscating the system that the modeling environment is attempting to represent. To correct this deficiency, we propose a Python-based "block-oriented" modeling approach for representing the discrete components within the system. Our approach is an extension of the Pyomo library for specifying mathematical optimization problems. Through the use of a modeling components library, the block-oriented approach facilitates a clean separation of system superstructure from the details of individual components. This approach also naturally lends itself to expressing design and operational decisions as disjunctive expressions over the component blocks. By expressing a mathematical optimization problem in a block-oriented manner, inherent structure (e.g., multiple scenarios) is preserved for potential exploitation by solvers. In particular, we show that block-structured mathematical optimization problems can be straightforwardly manipulated by decomposition-based multi-scenario algorithmic strategies, specifically in the context of the PySP stochastic programming library. We illustrate our block-oriented modeling approach using a case study drawn from the electricity grid operations domain: unit commitment with transmission switching and N - 1 reliability constraints. Finally, we demonstrate that the overhead associated with block-oriented modeling only minimally increases model instantiation times, and need not adversely impact solver behavior. (C) 2013 Elsevier Ltd. All rights reserved.
Ober-BlÃ¶baum, Sina
numerical methods have been de- veloped to compute trajectories of optimal control problems on the one hand optimal control problems. In this contribution we combine the optimal control method Discrete MechanicsSolving Multiobjective Optimal Control Problems in Space Mission Design using Discrete Mechanics
Multiresolution strategies for the numerical solution of optimal control problems
NASA Astrophysics Data System (ADS)
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a 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.
NASA Technical Reports Server (NTRS)
Tennille, Geoffrey M.; Howser, Lona M.
1993-01-01
The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.
Wu, Zong-Sheng; Fu, Wei-Ping; Xue, Ru
2015-01-01
Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well. PMID:26421005
Wu, Zong-Sheng; Fu, Wei-Ping; Xue, Ru
2015-01-01
Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well. PMID:26421005
Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron
2008-01-01
In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.
Duc T. Nguyen
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process
Bi-objective Optimization for the Vehicle Routing Problem with Time Windows
Bullinaria, John
Bi-objective Optimization for the Vehicle Routing Problem with Time Windows: Using Route Similarity. The Vehicle Routing Problem with Time Windows is a com- plex combinatorial optimization problem which can: Vehicle routing problem, multi-objective optimization, evolutionary algorithm, similarity of solutions. 1
Performance of quantum annealing in solving optimization problems: A review
NASA Astrophysics Data System (ADS)
Suzuki, S.
2015-02-01
Quantum annealing is one of the optimization method for generic optimization problems. It uses quantum mechanics and is implemented by a quantum computer ideally. At the earlier stage, several numerical experiments using conventional computers have provided results showing that quantum annealing produces an answer faster than simulated annealing, a classical counterpart of quantum annealing. Later, theoretical and numerical studies have shown that there are drawbacks in quantum annealing. The power of quantum annealing is still an open problem. What makes quantum annealing a hot topic now is that a quantum computer based on quantum annealing is manufactured and commercialized by a Canadian company named D-Wave Systems. In the present article, we review the study of quantum annealing, focusing mainly on its power.
Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem
NASA Technical Reports Server (NTRS)
Naidu, Desineni Subbaramaiah; Hibey, Joseph L.; Charalambous, Charalambos D.
1990-01-01
The optimal control problem arising in coplanar orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high to low earth orbit via the atmosphere, with the object of minimizing the total fuel consumption. Simulations are carried out to obtain the fuel-optimal trajectories for flying the spacecraft through the atmosphere. A highlight is the application of an efficient multiple-shooting method for treating the nonlinear two-point boundary value problem resulting from the optimizaion procedure. The strategy for the atmospheric portion of the minimum-fuel transfer is to fly at the maximum lift-to-drag ratio L/D initially in order to recover from the downward plunge, and then to fly at a negative L/D to level off the flight so that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.
Rigorous location of phase transitions in hard optimization problems.
Achlioptas, Dimitris; Naor, Assaf; Peres, Yuval
2005-06-01
It is widely believed that for many optimization problems, no algorithm is substantially more efficient than exhaustive search. This means that finding optimal solutions for many practical problems is completely beyond any current or projected computational capacity. To understand the origin of this extreme 'hardness', computer scientists, mathematicians and physicists have been investigating for two decades a connection between computational complexity and phase transitions in random instances of constraint satisfaction problems. Here we present a mathematically rigorous method for locating such phase transitions. Our method works by analysing the distribution of distances between pairs of solutions as constraints are added. By identifying critical behaviour in the evolution of this distribution, we can pinpoint the threshold location for a number of problems, including the two most-studied ones: random k-SAT and random graph colouring. Our results prove that the heuristic predictions of statistical physics in this context are essentially correct. Moreover, we establish that random instances of constraint satisfaction problems have solutions well beyond the reach of any analysed algorithm. PMID:15944693
Analog and digital FPGA implementation of BRIN for optimization problems.
Ng, H S; Lam, K P
2003-01-01
The binary relation inference network (BRIN) shows promise in obtaining the global optimal solution for optimization problem, which is time independent of the problem size. However, the realization of this method is dependent on the implementation platforms. We studied analog and digital FPGA implementation platforms. Analog implementation of BRIN for two different directed graph problems is studied. As transitive closure problems can transform to a special case of shortest path problems or a special case of maximum spanning tree problems, two different forms of BRIN are discussed. Their circuits using common analog integrated circuits are investigated. The BRIN solution for critical path problems is expressed and is implemented using the separated building block circuit and the combined building block circuit. As these circuits are different, the response time of these networks will be different. The advancement of field programmable gate arrays (FPGAs) in recent years, allowing millions of gates on a single chip and accompanying with high-level design tools, has allowed the implementation of very complex networks. With this exemption on manual circuit construction and availability of efficient design platform, the BRIN architecture could be built in a much more efficient way. Problems on bandwidth are removed by taking all previous external connections to the inside of the chip. By transforming BRIN to FPGA (Xilinx XC4010XL and XCV800 Virtex), we implement a synchronous network with computations in a finite number of steps. Two case studies are presented, with correct results verified from simulation implementation. Resource consumption on FPGAs is studied showing that Virtex devices are more suitable for the expansion of network in future developments. PMID:18244587
Optimization of Multiple Vehicle Routing Problems using Approximation Algorithms
Nallusamy, R; Dhanalaksmi, R; Parthiban, P
2010-01-01
This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the various heuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorit...
Advance ACO system in optimizing power system PMU placement problem
Bo Wang; Dichen Liu; Li Xiong
2009-01-01
GPS-based synchronous phasor measurement technology is a powerful tool for the security and reliable operation of the inter-connected electric power system. This paper presents an ACO-based approach to optimize the phasor measurement unit (PMU) placement problem. The pheromone trail persistence coefficient adaptive adjustment mechanism and stochastic perturbing progress are introduced into the ant colony system (ACS), in case the algorithm
Gaussian optimizers and the additivity problem in quantum information theory
NASA Astrophysics Data System (ADS)
Holevo, A. S.
2015-04-01
This paper surveys two remarkable analytical problems of quantum information theory. The main part is a detailed report on the recent (partial) solution of the quantum Gaussian optimizer problem which establishes an optimal property of Glauber's coherent states -- a particular case of pure quantum Gaussian states. The notion of a quantum Gaussian channel is developed as a non-commutative generalization of an integral operator with Gaussian kernel, and it is shown that the coherent states, and under certain conditions only they, minimize a broad class of concave functionals of the output of a Gaussian channel. Thus, the output states corresponding to a Gaussian input are the `least chaotic', majorizing all the other outputs. The solution, however, is essentially restricted to the gauge-invariant case where a distinguished complex structure plays a special role. Also discussed is the related well-known additivity conjecture, which was solved in principle in the negative some five years ago. This refers to the additivity or multiplicativity (with respect to tensor products of channels) of information quantities related to the classical capacity of a quantum channel, such as the (1\\to p)-norms or the minimal von Neumann or Rényi output entropies. A remarkable corollary of the present solution of the quantum Gaussian optimizer problem is that these additivity properties, while not valid in general, do hold in the important and interesting class of gauge-covariant Gaussian channels. Bibliography: 65 titles.
Solving Nonlinear Equality Constrained Multiobjective Optimization Problems Using Neural Networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques. PMID:25647664
Issues and Strategies in Solving Multidisciplinary Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya
2013-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
NASA Astrophysics Data System (ADS)
Gao, Qian
For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is compared with the conventional decoupled system with the same spectrum efficiency to demonstrate the power efficiency. Crucial lighting requirements are included as optimization constraints. To control non-linear distortion, the optical peak-to-average-power ratio (PAPR) of LEDs can be individually constrained. With a SVD-based pre-equalizer designed and employed, our scheme can achieve lower BER than counterparts applying zero-forcing (ZF) or linear minimum-mean-squared-error (LMMSE) based post-equalizers. Besides, a binary switching algorithm (BSA) is applied to improve BER performance. The third part looks into a problem of two-phase channel estimation in a relayed wireless network. The channel estimates in every phase are obtained by the linear minimum mean squared error (LMMSE) method. Inaccurate estimate of the relay to destination (RtD) channel in phase 1 could affect estimate of the source to relay (StR) channel in phase 2, which is made erroneous. We first derive a close-form expression for the averaged Bayesian mean-square estimation error (ABMSE) for both phase estimates in terms of the length of source and relay training slots, based on which an iterative searching algorithm is then proposed that optimally allocates training slots to the two phases such that estimation errors are balanced. Analysis shows how the ABMSE of the StD channel estimation varies with the lengths of relay training and source training slots, the relay amplification gain, and the channel prior information respectively. The last part deals with a transmission scheduling problem in a uplink multiple-input-multiple-output (MIMO) wireless network. Code division multiple access (CDMA) is assumed as a multiple access scheme and pseudo-random codes are employed for different users. We consider a heavy traffic scenario, in which each user always has packets to transmit in the scheduled time slots. If the relay is scheduled for transmission together with users, then it operates in a full-duplex mode, where the packets previously collected from users are transmitted to the destination
Convex bodies of states and maps
Janusz Grabowski; Alberto Ibort; Marek Ku?; Giuseppe Marmo
2013-06-13
We give a general solution to the question 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 states. 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 properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of 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.
Dual Population-Based Incremental Learning for Problem Optimization in Dynamic Environments
Yang, Shengxiang
Dual Population-Based Incremental Learning for Problem Optimization in Dynamic Environments: dynamic optimization, population-based incremental learning, dualism, evolutionary algorithms 1 of Population-Based Incremental Learning (PBIL) algorithms, a class of EAs, for solving dynamic optimization
Ren, Yuan
2010-01-14
This dissertation presents an algorithm to solve optimization problems with "black-box" objective functions, i.e., functions that can only be evaluated by running a computer program. Such optimization problems often arise ...
ADMM for Sparse Semidefinite Programming with Applications to Optimal Power Flow Problem
Lavaei, Javad
1 ADMM for Sparse Semidefinite Programming with Applications to Optimal Power Flow Problem Ramtin applied to the SDP relaxation of the optimal power flow (OPF) problem, and tested on the IEEE benchmark
Multi-objective evolutionary methods for time-changing portfolio optimization problems
Hatzakis, Iason
2007-01-01
This thesis is focused on the discovery of efficient asset allocations with the use of evolutionary algorithms. The portfolio optimization problem is a multi-objective optimization problem for the conflicting criteria of ...
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems.
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification. PMID:26336509
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification. PMID:26336509
Left ventricle segmentation in MRI via convex relaxed distribution matching.
Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben
2013-12-01
A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm. PMID:23851075
Optimality Conditions for A Two-Stage Reservoir Operation Problem
NASA Astrophysics Data System (ADS)
Zhao, J.; Cai, X.; Wang, Z.
2010-12-01
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.
A mathematical programming approach to stochastic and dynamic optimization problems
Bertsimas, D.
1994-12-31
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.
Resource efficient gadgets for compiling adiabatic quantum optimization problems
NASA Astrophysics Data System (ADS)
Babbush, Ryan; O'Gorman, Bryan; Aspuru-Guzik, Alán
2013-11-01
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.
On the robust optimization to the uncertain vaccination strategy problem
NASA Astrophysics Data System (ADS)
Chaerani, D.; Anggriani, N.; Firdaniza
2014-02-01
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.
On the robust optimization to the uncertain vaccination strategy problem
Chaerani, D. Anggriani, N. Firdaniza
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
Algorithms for bilevel optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.
New attitude penalty functions for spacecraft optimal control problems
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)
1996-03-01
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}.
Symmetry of Solutions to the Generalized 1-D Optimal Sojourn Time Control Problem
Zhang, Wei
Symmetry of Solutions to the Generalized 1-D Optimal Sojourn Time Control Problem Wei Zhang70, jianghai}@purdue.edu Abstract-- The optimal sojourn time control (OSTC) problem tries to find the optimal sojourn time control (OSTC) problem, and will be the focus of this paper. While the general
Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
Lavaei, Javad
1 Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem Ramtin Madani optimal power flow (SCOPF) problem, where each contingency corresponds to the outage of an arbitrary verified in over 7000 simulations). The major drawback of representing the optimal power flow problem
Network Topologies Guaranteeing Zero Duality Gap for Optimal Power Flow Problem
Lavaei, Javad
1 Network Topologies Guaranteeing Zero Duality Gap for Optimal Power Flow Problem Somayeh Sojoudi and Javad Lavaei Abstract--We have recently shown that the optimal power flow (OPF) problem with a quadratic power flow (OPF) problem is concerned with finding an optimal operating point of a power system, which
NASA Astrophysics Data System (ADS)
Izui, K.; Nishiwaki, S.; Yoshimura, M.
2007-12-01
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.
Near-optimal perfectly matched layers for indefinite Helmholtz problems
Vladimir Druskin; Stefan Güttel; Leonid Knizhnerman
2015-07-22
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the union of a negative and positive real interval, designed with the help of a classical result by Zolotarev. Using Krein's interpretation of a Stieltjes continued fraction, this interpolant can be converted into a three-term finite difference discretization of a perfectly matched layer (PML) which converges exponentially fast in the number of grid points. The convergence rate is asymptotically optimal for both propagative and evanescent wave modes. Several numerical experiments and illustrations are included.
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
Solving the Attribute Reduction Problem with Ant Colony Optimization
NASA Astrophysics Data System (ADS)
Yu, Hong; Wang, Guoyin; Lan, Fakuan
Attribute reduction is an important process in rough set theory. More minimal attribute reductions are expected to help clients make decisions in some cases, though the minimal attribute reduction problem (MARP) is proved to be an NP-hard problem. In this paper, we propose a new heuristic approach for solving the MARP based on the ant colony optimization (ACO) metaheuristic. We first model the MARP as finding an assignment which minimizes the cost in a graph. Afterward, we introduce a preprocessing step that removes the redundant data in a discernibility matrix through the absorption operator and the cutting operator, the goal of which is to favor a smaller exploration of the search space at a lower cost. We then develop a new algorithm R-ACO for solving the MARP. Finally, the simulation results show that our approach can find more minimal attribute reductions more efficiently in most cases.
Radio interferometric gain calibration as a complex optimization problem
NASA Astrophysics Data System (ADS)
Smirnov, O. M.; Tasse, C.
2015-05-01
Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as STEFCAL and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of COHJONES, another specialized direction-dependent calibration algorithm derived from the formalism.
Searching in an Unknown Environment: An Optimal Randomized Algorithm for the Cow-Path Problem
Tate, Steve
Searching in an Unknown Environment: An Optimal Randomized Algorithm for the Cow-Path Problem Ming in mind, the abstract problem known as the w-lane cow-path problem was designed. There are known optimal deterministic algorithms for the cow-path problem, and we give the first randomized algorithm in this paper. We
A sparse superlinearly convergent SQP with applications to two-dimensional shape optimization.
Anitescu, M.
1998-04-15
Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem.
Chandrasekaran, Venkat
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 ...
Generalized convexity and inequalities
NASA Astrophysics Data System (ADS)
Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.
2007-11-01
Let and let be the family of all mean values of two numbers in (some examples are the arithmetic, geometric, and harmonic means). Given , we say that a function is (m1,m2)-convex if f(m1(x,y))[less-than-or-equals, slant]m2(f(x),f(y)) for all . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.
Logical definability and asymptotic growth in optimization and counting problems
Compton, K. [Univ. of Michigan, Ann Arbor, MI (United States)
1994-12-31
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.
Hybrid Unicast and Multicast Flow Control: A Linear Optimization Approach
Yousefi'zadeh, Homayoun; Fazel, Fatemeh; Jafarkhani, Hamid
2004-01-01
of “Flow Control Optimization Algorithm” is linear in termscontrol prob- lem is a convex optimization problem de?ned over a set of piecewise linearlinear programming schemes and water-?lling scheme re- spectively, our solutions to centralized and decentralized for- mulations of the ?ow control
Convex Onion Peeling Genetic Algorithm: An Efficient Solution to Map Labeling of Point-Feature
Bae, Wan
Convex Onion Peeling Genetic Algorithm: An Efficient Solution to Map Labeling of Point-Feature Wan-feature and develop a new genetic algorithm to solve this problem. We adopt a data struc- ture called convex onion peeling and utilize it in our pro- posed Convex Onion Peeling Genetic Algorithm (COPGA) to efficiently
Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation
NASA Astrophysics Data System (ADS)
Kmet', Tibor; Kmet'ov, Mria
2010-09-01
A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.
One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics
Zaslavski, Alexander J.
2011-12-15
We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.
Lavaei, Javad
1 Convexification of Optimal Power Flow Problem by Means of Phase Shifters Somayeh Sojoudi with the convexification of the optimal power flow (OPF) problem. We have previously shown that this highly nonconvex few minutes to every several months. State estimation, optimal power flow (OPF), security
Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low
Low, Steven H.
1 Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low Abstract--The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose-negativity of physical quantities such as resistance and inductance. Index Terms--Power System, Optimal Power Flow
Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
Lavaei, Javad
Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem Ramtin Madani optimal power flow (SCOPF) problem, where each contingency corresponds to the outage of an arbitrary-sized systems (as verified in 7000 simulations). The major drawback of representing the optimal power flow
Kunkel, Peter
The linear quadratic optimal control problem for linear descriptor systems with variable coefficients Peter Kunkel 3 Volker Mehrmann y 17.01.97 Abstract We study linear quadratic optimal control, 93B11, 93B40 1 Introduction In this paper we study the linearÂquadratic optimal control problem
Hauck, Cory D [ORNL; Alldredge, Graham [University of Maryland; Tits, Andre [University of Maryland
2012-01-01
We present a numerical algorithm to implement entropy-based (M{sub N}) moment models in the context of a simple, linear kinetic equation for particles moving through a material slab. The closure for these models - as is the case for all entropy-based models - is derived through the solution of constrained, convex optimization problem. The algorithm has two components. The first component is a discretization of the moment equations which preserves the set of realizable moments, thereby ensuring that the optimization problem has a solution (in exact arithmetic). The discretization is a second-order kinetic scheme which uses MUSCL-type limiting in space and a strong-stability-preserving, Runge-Kutta time integrator. The second component of the algorithm is a Newton-based solver for the dual optimization problem, which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives. The accuracy of the numerical solution to the dual problem plays a key role in the time step restriction for the kinetic scheme. We study in detail the difficulties in the dual problem that arise near the boundary of realizable moments, where quadrature formulas are less reliable and the Hessian of the dual objection function is highly ill-conditioned. Extensive numerical experiments are performed to illustrate these difficulties. In cases where the dual problem becomes 'too difficult' to solve numerically, we propose a regularization technique to artificially move moments away from the realizable boundary in a way that still preserves local particle concentrations. We present results of numerical simulations for two challenging test problems in order to quantify the characteristics of the optimization solver and to investigate when and how frequently the regularization is needed.
Li, Yangmin
Cooperative Particle Swarm Optimizer with Elimination Mechanism for Global Optimization particle swarm optimizer (PSO) that called the cooperative particle swarm optimizer with elimination. I. INTRODUCTION IN the past decade, particle swarm optimizer (PSO) has been applied and studied
Human opinion dynamics: an inspiration to solve complex optimization problems.
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P; Kapur, Pawan
2013-01-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making. PMID:24141795
Human opinion dynamics: An inspiration to solve complex optimization problems
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan
2013-01-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making. PMID:24141795
A relaxed reduced space SQP strategy for dynamic optimization problems.
Logsdon, J. S.; Biegler, L. T.; Carnegie-Mellon Univ.
1993-01-01
Recently, strategies have been developed to solve dynamic simulation and optimization problems in a simultaneous manner by applying orthogonal collocation on finite elements and solving the nonlinear program (NLP) with a reduced space successive quadratic programming (SQP) approach. We develop a relaxed simultaneous approach that leads to faster performance. The method operates in the reduced space of the control variables and solves the collocation equations inexactly at each SQP iteration. Unlike previous simultaneous formulations, it is able to consider the state variables one element at a time. Also, this approach is compared on two process examples to the reduced gradient, feasible path approach outlined in Logsdon and Biegler. Nonlinear programs with up to 5500 variables are solved with only 40% of the effort. Finally, a theoretical analysis of this approach is provided.
The International Solar Polar Mission - A problem in constrained optimization
NASA Technical Reports Server (NTRS)
Sweetser, T. H., III; Parmenter, M. E.; Pojman, J. L.
1981-01-01
The International Solar Polar Mission is sponsored jointly by NASA and the European Space Agency to study the sun and the solar environment from a new vantage point. Trajectories far out of the ecliptic plane are achieved by a gravity assist from Jupiter which sends the spacecraft back over the poles of the sun. The process for optimizing these trajectories is described. From the point of view of trajectory design, performance is measured by the time spent at high heliographic latitudes, but many trajectory constraints must be met to ensure spacecraft integrity and good scientific return. The design problem is tractable by closely approximating integrated trajectories with specially calibrated conics. Then the optimum trajectory is found primarily by graphical methods, which were easy to develop and use and are highly adaptable to changes in the plan of the mission.
Disjunctive Cuts for Non-convex Mixed Integer Quadratically Constrained Programs
Anureet Saxena; Pierre Bonami; Jon Lee
2008-01-01
This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming\\u000a (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and\\u000a non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming\\u000a and the lift-and-project methodology. In particular, we propose new methods for
S. Kannan; S. Mary Raja Slochanal; P. Subbaraj; Narayana Prasad Padhy
2004-01-01
This paper presents the application of particle swarm optimization (PSO) technique and its variants to least-cost generation expansion planning (GEP) problem. The GEP problem is a highly constrained, combinatorial optimization problem that can be solved by complete enumeration. PSO is one of the swarm intelligence (SI) techniques, which use the group intelligence behavior along with individual intelligence to solve the
Statics and asymptotics of a price control limit: an optimal timing inventory problem
Haase, Markus
Statics and asymptotics of a price control limit: an optimal timing inventory problem R.O. Davies begin by describing two inter-related inventory optimization problems, both of which identify a critical by asymptotic analysis), and ...nally outline the structure of the paper. Our two inventory problems both have
An Efficient Method for Large Margin Parameter Optimization in Structured Prediction Problems
Yu, Huizhen Janey
An Efficient Method for Large Margin Parameter Optimization in Structured Prediction Problems Abstract We consider structured prediction problems with a parametrized linear prediction function, and the associated parameter optimization problems in large margin type of discriminative training. We propose a dual
CASE STUDIES IN OPTIMIZATION: CATENARY PROBLEM IGOR A. GRIVA AND ROBERT J. VANDERBEI
Vanderbei, Robert J.
CASE STUDIES IN OPTIMIZATION: CATENARY PROBLEM IGOR A. GRIVA AND ROBERT J. VANDERBEI Operations optimization. 1 #12;2 IGOR A. GRIVA AND ROBERT J. VANDERBEI restrictive for modern engineering. Moreover
Generalized vector calculus on convex domain
NASA Astrophysics Data System (ADS)
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
On the application of deterministic optimization methods to stochastic control problems
NASA Technical Reports Server (NTRS)
Kramer, L. C.; Athans, M.
1974-01-01
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
Kearfott, R. Baker
) The optimum and at least one optimizing point for convex nonlinear programs can be ap- proximated well by the solution to a linear program (a fact long used in branch and bound algorithms). In more general problems of a single linear program. If these subspaces are low-dimensional, this suggests subdividing the variables
Advancement and analysis of Gauss pseudospectral transcription for optimal control problems
Huntington, Geoffrey Todd, 1979-
2007-01-01
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 ...
Continuous Blooming of Convex Polyhedra
Demaine, Erik D.
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number ...
Complete Search in Continuous Global Optimization
Neumaier, Arnold
as a text for teaching constrained global optimization. After motivation for and important examples and recipes for their use in the constrained case follows, an explicit example is discussed, introducing. Then a discussion of important problem transformations follows, in particular of linear, convex, and semilinear
Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy
de Leon, Alex R.
Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework for inverse radiotherapy treatment planning, with a special focus on IMRT as being one planning station. Keywords: radiotherapy optimization, IMRT, DVH, gEUD, GMC, inverse planning, convex
New approach for the solution of optimal control problems on parallel machines. Doctoral thesis
Stech, D.J.
1990-01-01
This thesis develops a highly parallel solution method for nonlinear optimal control problems. Balakrishnan's epsilon method is used in conjunction with the Rayleigh-Ritz method to convert the dynamic optimization of the optimal control problem into a static optimization problem. Walsh functions and orthogonal polynomials are used as basis functions to implement the Rayleigh-Ritz method. The resulting static optimization problem is solved using matrix operations which have well defined massively parallel solution methods. To demonstrate the method, a variety of nonlinear optimal control problems are solved. The nonlinear Raleigh problem with quadratic cost and nonlinear van der Pol problem with quadratic cost and terminal constraints on the states are solved in both serial and parallel on an eight processor Intel Hypercube. The solutions using both Walsh functions and Legendre polynomials as basis functions are given. In addition to these problems which are solved in parallel, a more complex nonlinear minimum time optimal control problem and nonlinear optimal control problem with an inequality constraint on the control are solved. Results show the method converges quickly, even from relatively poor initial guesses for the nominal trajectories.
Convex Geometry and Stoichiometry
Jer-Chin,
2011-01-01
We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.
Lift-and-Project Cuts for Mixed Integer Convex Programs
Pierre Bonami
\\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
OPTIMAL CONTROL PROBLEMS WITH FINAL OBSERVATION GOVERNED BY EXPLOSIVE PARABOLIC EQUATIONS
Amann, Herbert
OPTIMAL CONTROL PROBLEMS WITH FINAL OBSERVATION GOVERNED BY EXPLOSIVE PARABOLIC EQUATIONS H. AMANN]), then the sequence (y(uk)) is bounded and standard compactness results for the state problem enable us to pass
OPTIMAL CONTROL PROBLEMS WITH FINAL OBSERVATION GOVERNED BY EXPLOSIVE PARABOLIC EQUATIONS
Amann, Herbert
OPTIMAL CONTROL PROBLEMS WITH FINAL OBSERVATION GOVERNED BY EXPLOSIVE PARABOLIC EQUATIONS H. AMANN, T ]), then the sequence (y(u k )) is bounded and standard compactness results for the state problem enable us to pass
Study on Two Optimization Problems: Line Cover and Maximum Genus Embedding
Cao, Cheng
2012-07-16
In this thesis, we study two optimization problems which have a lot of important applications in diverse domains: Line Cover Problem (LCP) in Computational Geometry and Maximum Genus Embedding (MGE) in Topological Graph Theory. We study LCP whose...
An Exact Algorithm for Optimal Areal Positioning Problem with Rectangular Targets and Requests
Bansal, Manish
2011-02-22
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, ...
Bertsimas, Dimitris J.
Our interest lies in solving sum of squares (SOS) relaxations of large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, ...
Flow Control as Stochastic Optimal Control Problem with Incomplete Information
Avrachenkov, Konstantin
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
Nonconvex network optimization: Algorithms and software
Lamar, B.
1994-12-31
Although very efficient solution methods exist for linear and convex network optimization problems, minimum cost network flow problems with concave arc cost functions are challenging because the determination of the optimal solution requires, in the worst case, an evaluation of all the extreme points in the feasible region. Even more challenging, are network flow problems whose arc costs are neither concave nor convex as is the case for problems with price breaks or all-unit discounting. Yet, such situations arise frequently in many real-world problems. In this talk, solution methods for concave cost network flow problems will be reviewed and a computer software package will be presented. In addition, a method for converting networks with arbitrary arc costs into a pure concave cost network will be described.
NSDL National Science Digital Library
Tim Lambert
An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from different directions; see how the gift-wrapping or divide-and-conquer algorithms construct the hull; look at animations of Delaunay triangulation algorithms.
AN ANT COLONY OPTIMIZATION APPROACH FOR THE CAPACITATED VEHICLE ROUTING PROBLEM WITH
Yanikoglu, Berrin
AN ANT COLONY OPTIMIZATION APPROACH FOR THE CAPACITATED VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS to the NP- hard Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP). In VRPSDP of the benchmark problems in the literature. 1. Introduction The Vehicle Routing Problem with Simultaneous Delivery
NASA Astrophysics Data System (ADS)
Bera, Sasadhar; Mukherjee, Indrajit
2010-10-01
Ensuring quality of a product is rarely based on observations of a single quality characteristic. Generally, it is based on observations of family of properties, so-called `multiple responses'. These multiple responses are often interacting and are measured in variety of units. Due to presence of interaction(s), overall optimal conditions for all the responses rarely result from isolated optimal condition of individual response. Conventional optimization techniques, such as design of experiment, linear and nonlinear programmings are generally recommended for single response optimization problems. Applying any of these techniques for multiple response optimization problem may lead to unnecessary simplification of the real problem with several restrictive model assumptions. In addition, engineering judgements or subjective ways of decision making may play an important role to apply some of these conventional techniques. In this context, a synergistic approach of desirability functions and metaheuristic technique is a viable alternative to handle multiple response optimization problems. Metaheuristics, such as simulated annealing (SA) and particle swarm optimization (PSO), have shown immense success to solve various discrete and continuous single response optimization problems. Instigated by those successful applications, this chapter assesses the potential of a Nelder-Mead simplex-based SA (SIMSA) and PSO to resolve varied multiple response optimization problems. The computational results clearly indicate the superiority of PSO over SIMSA for the selected problems.
A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo
1996-01-01
A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.
Jacobian Singularities in Optimal Power Flow Problems Caused by Intertemporal Constraints
Li, Xin
Jacobian Singularities in Optimal Power Flow Problems Caused by Intertemporal Constraints Kyri, Senior Member, IEEE. Abstract--In multi-timestep Optimal Power Flow (OPF) for- mulations, constraints on the Newton-Raphson al- gorithm are widely used to solve Optimal Power Flow (OPF) and Economic Dispatch
Relaxations for multi-period optimal power flow problems with discrete decision variables
Ernst, Damien
Relaxations for multi-period optimal power flow problems with discrete decision variables Q. Gemine--We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service relaxation are significantly less violated. Index Terms--Multi-period optimal power flow; relaxation schemes
Gravdahl, Jan Tommy
-Time Algorithm for Determining the Optimal Paint Gun Orientation in Spray Paint Applications Pål Johan From of finding the optimal orientation at every time step into a convex optimization problem that can be solved in the end-effector orientation improves per- formance, such as welding and high-pressure water steaming
Learning the Dominance in Diploid Genetic Algorithms for Changing Optimization Problems
Yang, Shengxiang
Learning the Dominance in Diploid Genetic Algorithms for Changing Optimization Problems Shengxiang Yang Abstract-- Using diploid representation with dominance scheme is one of the approaches developed for genetic al- gorithms to address dynamic optimization problems. This paper proposes an adaptive dominance
Cláudio M. N. A. Pereira; Celso M. F. Lapa
2003-01-01
This work extends the research related to genetic algorithms (GA) in core design optimization problems, which basic investigations were presented in previous work. Here we explore the use of the Island Genetic Algorithm (IGA), a coarse-grained parallel GA model, comparing its performance to that obtained by the application of a traditional non-parallel GA. The optimization problem consists on adjusting several
State and Parameter Estimation in Nonlinear Systems as an Optimal Tracking Problem
Gill, Philip E.
as a function of the model parameters) is ill-defined. In addition, for large enough coupling, the data entrainState and Parameter Estimation in Nonlinear Systems as an Optimal Tracking Problem Daniel R solution. In particular, we show the equivalence of this problem to that of tracking within an optimal
Optimization of the shape and the location of the actuators in an internal control problem.
Maillot, HervÃ?Â©
as a static model problem for classical control problems when we look for the optimal location of the actuators in some stabilization equations. Concerning our optimization criterion, the term #31; ! u 2 can cannot apply their general result and we need to use a relaxed formulation. Since the shape variable
SOLUTION OF OPTIMAL CONTROL PROBLEMS BY A POINTWISE PROJECTED NEWTON METHOD
SOLUTION OF OPTIMAL CONTROL PROBLEMS BY A POINTWISE PROJECTED NEWTON METHOD C.T. KELLEY \\Lambda of the projected Newton method of Bertsekas. The estimates are also valid for discretized versions of the methodÂproblem pair. Key words. projected Newton iteration, optimal control AMS(MOS) subject classifications. 47H17
20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev
Dimov, Ivan
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
Exploiting problem structure in pattern-search methods for unconstrained optimization
Toint, Philippe
Exploiting problem structure in pattern-search methods for unconstrained optimization by C. Price 1.toint@fundp.ac.be #12; Exploiting problem structure in pattern-search methods for unconstrained optimization C. J. Price structure of the objective function to be exploited. This has two advantages: it reduces the work needed
Optimal Conditions for the Control Problem Associated to a Biomedical Process
NASA Astrophysics Data System (ADS)
Bund?u, O.; Juratoni, A.; Chevere?an, A.
2010-09-01
This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.
Investigation of the optimal control problem for metal solidification in a new formulation
NASA Astrophysics Data System (ADS)
Albu, A. F.; Zubov, V. I.
2014-05-01
New formulations of the optimal control problem for metal solidification in a furnace are proposed and studied. The underlying mathematical model of the process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The formulated problems are solved numerically with the help of gradient optimization methods. The gradient of the cost function is computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for a chosen discrete version of the optimal control problem. The research results are described and analyzed. Some of the results are illustrated.
Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)
2005-04-01
We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process
Robust Approximate Optimization for Large Scale Planning Problems Marek Petrik
Shenoy, Prashant
is extremely general in terms of its expressive power almost every problem can be mapped easily into an MDP power-plant management, and managing blood inventories [Powell, 2007]. While these problems are easy
Solving the facility and layout and location problem by ant-colony optimization-meta heuristic
Hamid Davoud Pour; Mostafa Nosraty
2006-01-01
This paper describes a heuristic algorithm for solving the plant\\/facility location problem by applying ant-colony optimization meta-heuristic. The facility location problem is discussed, and a mathematical formulation is presented. The problem is then modelled as a quadratic assignment problem. An ant algorithm is developed to solve the problem. The results reveal that the proposed algorithm can be adaptively constructed to
Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling
Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang
2014-01-01
A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220
Solving constraint satisfaction and optimization problems by a neuro-fuzzy approach.
Cavalieri, S; Russo, M
1999-01-01
The solution of constrained satisfaction and constrained optimization problems using a Hopfield model requires determination of the values of a certain number of coefficients linked to the surrounding conditions of the problem. It is quite difficult to determine these values, mainly because a heuristic search is necessary. This is not only time-consuming but may lead to solutions that are far from optimal, or even nonvalid ones. So far, there have been no works in literature offering a general method for the search for coefficents with will guarantee optimal or close to optimal solutions. This paper proposes a fuzzy approach which allows automatic determination of Hopfield coefficients. PMID:18252367
A Collection of Challenging Optimization Problems in Science, Engineering and Economics
Mehta, Dhagash
2015-01-01
Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will n...
A hybrid Honey Bees Mating Optimization algorithm for the Probabilistic Traveling Salesman Problem
Yannis Marinakis; Magdalene Marinaki
2009-01-01
The probabilistic traveling salesman problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In this paper, a new hybrid algorithmic nature inspired approach based on honey bees mating optimization (HBMO), greedy randomized adaptive search procedure (GRASP) and expanding neighborhood search strategy (ENS) is proposed for the solution of the probabilistic
Discrete Optimization Arc routing problems with time-dependent service costs
Potvin, Jean-Yves
of classical instances of the vehicle routing problem with time windows. Ó 2006 Elsevier B.V. All rights instances of the vehicle routing problem with time windows (VRPTWs) are reported [26]. FinallyDiscrete Optimization Arc routing problems with time-dependent service costs Mariam Tagmouti
Discrete Optimization An exact algorithm for a single-vehicle routing problem
Potvin, Jean-Yves
Discrete Optimization An exact algorithm for a single-vehicle routing problem with time windows from benchmark instances of the classical vehicle routing problem with time windows. Ó 2006 Elsevier B; Elementary shortest paths 1. Introduction In this work, we consider a variant of the vehicle routing problem
Singular optimal control and the identically non-regular problem in the calculus of variations
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.
1985-01-01
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Parallel Multi-Swarm Optimization Framework for Search Problems in Water Distribution Systems
Parallel Multi-Swarm Optimization Framework for Search Problems in Water Distribution Systems Sarat concurrent particle swarms is developed and applied to water distribution problems. Details of the enabling characterization problems for two water distribution networks with 1,834 and 12,457 nodes respectively. 1
Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity
NASA Astrophysics Data System (ADS)
Briec, Walter; Horvath, Charles
2008-05-01
-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.
A Numerical Method to solve Optimal Transport Problems with Coulomb Cost
Jean-David Benamou; Guillaume Carlier; Luca Nenna
2015-05-07
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases.
Discrete-time entropy formulation of optimal and adaptive control problems
NASA Technical Reports Server (NTRS)
Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.
1992-01-01
The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.
Optimal Algorithms for the Economic Lot-Sizing Problem with Multi-supplier
NASA Astrophysics Data System (ADS)
Bai, Qing-Guo; Xu, Jian-Teng
This paper considers the economic lot-sizing problem with multi-supplier in which the retailer may replenish his inventory from several suppliers. Each supplier is characterized by one of two types of order cost structures: incremental quantity discount cost structure and multiple set-ups cost structure. The problem is challenging due to the mix of different cost structures. By analyzing the optimal properties, we reduce the searching range of the optimal solutions and develop several optimal algorithms to solve all cases of this multi-supplier problem.
Bukhsh, Waqquas Ahmed
2014-07-01
Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow ...
NASA Astrophysics Data System (ADS)
Lim, Byung Hwa; Shin, Yong Hyun; Choi, U. Jin
2008-09-01
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.
Glineur, François
Linearization of Second-Order Cone Limit Analysis Problems ·First ·Prev ·Next ·Last ·Go Back ·Full;Linearization of Second-Order Cone Limit Analysis Problems ·First ·Prev ·Next ·Last ·Go Back ·Full Screen ·Close Problems ·First ·Prev ·Next ·Last ·Go Back ·Full Screen ·Close ·Quit Introduction Convex optimization Let f
Regression model based on convex combinations best correlated with response
NASA Astrophysics Data System (ADS)
Dokukin, A. A.; Senko, O. V.
2015-03-01
A new regression method based on constructing optimal convex combinations of simple linear regressions of the least squares method (LSM regressions) built from original regressors is presented. It is shown that, in fact, this regression method is equivalent to a modification of the LSM including the additional requirement of the coincidence of the sign of the regression parameter with that of the correlation coefficient between the corresponding regressor and the response. A method for constructing optimal convex combinations based on the concept of nonexpandable irreducible ensembles is described. Results of experiments comparing the developed method with the known glmnet algorithm are presented, which confirm the efficiency of the former.
Solving the optimal attention allocation problem in manual control
NASA Technical Reports Server (NTRS)
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
Necessary conditions for multiobjective optimal control problems with state constraints
Wong, Ngai-Ching
by Ioffe [9], Loewen and Rockafellar [11], Vinter and Zheng [26] for problems with unbounded differential. This result was extended by Bellaassali and Jourani [2]. Based on an analysis of Ioffe's scheme [9 the necessary conditions for (P), we will use a variant of Ioffe's scheme to reduce the problem to the scalar
Nonlinear switched capacitor `neural' networks for optimization problems
A. Rodriguez-Vazquez; R. Dominguez-Castro; A. Rueda; J. L. Huertas; E. Sanchez-Sinencio
1990-01-01
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.
Oliveira, Ivan B. (Ivan Borges), 1975-
2002-01-01
Optimal control problems often arise in engineering applications when a known desired behavior is to be imposed on a dynamical system. Typically, there is a performance and controller use trade-off that can be quantified ...
Measures and LMI for impulsive optimal control with applications to space rendezvous problems
Claeys, Mathieu; Henrion, Didier; Lasserre, Jean-Bernard
2011-01-01
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control problem into a measure differential problem. The manipulation of the measures by their moments reduces the problem to a convergent series of standard linear matrix inequality (LMI) relaxations. After providing numerous academic examples, we apply the method to the impulsive rendezvous of two orbiting spacecrafts. As the method provides lower bounds on the global infimum, global optimality of the solutions can be guaranteed numerically by a posteriori simulations, and we can recover simultaneously the optimal impulse time and amplitudes by simple linear algebra.
Structure-exploiting interior point methods for security constrained optimal power flow problems
Chiang, Naiyuan
2013-07-01
The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods ...
A SHARP NON-CONVEXITY BOUND FOR PARTITION RANGES OF VECTOR MEASURES WITH ATOMS
Allaart, Pieter
A SHARP NON-CONVEXITY BOUND FOR PARTITION RANGES OF VECTOR MEASURES WITH ATOMS PIETER C. ALLAART of the atoms of that measure. This upper bound improves on a bound of Hill and Tong (1989) by an order and phrases. Partition range, optimal-partitioning, convexity theorem, vector mea- sure, vector atom, Hausdor
Discrete Optimization. Lecture Notes 7 Solution Methods for Discrete Problems
Damaschke, Peter
", since there is a chance that Sw contains an optimal solution. The search stops when only one active leaf represents the entire S, and the leafs represent single solutions. Branching alone would be useless. We do tree, with Sr := S and we set r "active". In every step, some active node v is chosen and set "inactive
UNIFIED PARTICLE SWARM OPTIMIZATION FOR TACKLING OPERATIONS RESEARCH PROBLEMS
Parsopoulos, Konstantinos
of the variables are real, will be considered in future works. Particle Swarm Optimization (PSO) has proved as a unified PSO scheme that com- bines the exploration and exploitation properties of differ- ent PSO variants of UPSO against the standard PSO variants [7, 8]. We investigate the performance of UPSO on minimax
Some Marginalist Intuition Concerning the Optimal Commodity Tax Problem
ERIC Educational Resources Information Center
Brett, Craig
2006-01-01
The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…
Solving static output feedback problems by direct search optimization
Henrion, Didier
, computer-aided control system design. I. INTRODUCTION In [3], N. J. Higham proposed to use direct search optimization, investigating questions on stability and accuracy of numerical algorithms in matrix computations. The purpose of this note is to report numerical experiments showing that with these routines a non-expert user
Selected Open Problems in Discrete Geometry and Optimization
de Leon, Alex R.
@mcmaster.ca Y. Ye Department of Management Science and Engineering, Huang Engineering Center 308, School of Engineering, Stanford University, Stanford, 475 Via Ortega, CA 94305, USA e-mail: yinyu-ye@stanford.edu K Geometry and Optimization 323 dimensions are motivated by the well-known solution (attributed to A. Tarski
Existence of Optimal Strategies for a Fire Confinement Problem
Bressan, Alberto
. In this paper we prove the existence of an optimal strategy, which minimizes the value of the area destroyed by the fire, plus the cost of constructing the barrier. 1 Introduction Aim of this paper is to analyze a new is either soaked with water poured from above (by airplane or helicopter), or cleared from all vegetation
Phase Transitions in Optimization Problems Alexander K. Hartmann
Peinke, Joachim
"Complex behavior of discrete systems in Physics, Biology, Mathematcs and Computer Science" Computer;Research Group Computational Physics "Complex behavior of discrete systems in Physics, Biology, Mathematcs Simulations New algorithms few group members Optimization algorithms Development/application 2 / 25 #12
An Optimization Software to solve Employee Timetabling Problems: OPTIHPER
Barber, Federico
satisfaction is a fundamental factor for the success of a company. This fact directly implies the consideration-objective function to be optimized. The main objective is to determine the best assignment that verifies and a multi- criteria objective function. A customized version of this system is used with very satisfactory
Parallel evolutionary algorithms for optimization problems in aerospace engineering
J. F. Wang; J. Periaux; M. Sefrioui
2002-01-01
This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of
Optimizing completely positive maps using semidefinite programming
NASA Astrophysics Data System (ADS)
Audenaert, Koenraad; de Moor, Bart
2002-03-01
Recently, a lot of attention has been devoted to finding physically realizable operations that realize as closely as possible certain desired transformations between quantum states, e.g., quantum cloning, teleportation, quantum gates, etc. Mathematically, this problem boils down to finding a completely positive trace-preserving (CPTP) linear map that maximizes the (mean) fidelity between the map itself and the desired transformation. In this communication, we want to draw attention to the fact that this problem belongs to the class of so-called semidefinite programming (SDP) problems. As SDP problems are convex, it immediately follows that they do not suffer from local optima. Furthermore, this implies that the numerical optimization of the CPTP map can, and should, be done using methods from the well-established SDP field, as these methods exploit convexity and are guaranteed to converge to the real solution. Finally, we show how the duality inherent to convex and SDP problems can be exploited to prove analytically the optimality of a proposed solution. We give an example of how to apply this proof method by proving the optimality of Hardy and Song's optimal qubit ? shifter (e-print quant-ph/0102100).
A Hybrid Ant Colony Optimization and Its Application to Vehicle Routing Problem with Time Windows
Xiangpei Hu; Qiulei Ding; Yunzeng Wang
\\u000a The Ant Colony Optimization (ACO) is a recent meta-heuristic algorithm for solving hard combinatorial optimization problems.\\u000a The algorithm, however, has the weaknesses of premature convergence and low search speed, which greatly hinder its application.\\u000a In order to improve the performance of the algorithm, a hybrid ant colony optimization (HACO) is presented by adjusting pheromone\\u000a approach, introducing a disaster operator, and
Computing Optimal Islands C. Bautista
Díaz-Báñez, José Miguel
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
Strengthening the conditions of Clarke and Smirnov for convex-valued differential inclusions
Milyutin, A A [N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow (Russian Federation)
2003-02-28
Assume that a Lipschitz continuous differential inclusion with convex images and locally compact graph is fixed on a certain time interval. For trajectories of this inclusion the problem of the minimization of a smooth end-point function is considered under smooth end-point constraints of equality and inequality types. This problem is approximated by a sequence of smooth optimal control problems with regular mixed constraints, which are treated using the maximum principle obtained earlier by the author in conjunction with Dubovitskii. Passing to the limit in the conditions of the maximum principle one obtains necessary conditions for strong minimality in the initial problem which refine the well-known conditions of Clarke and Smirnov.
Discrete Optimization Tabu search and GRASP for the maximum diversity problem
Duarte, Abraham
Discrete Optimization Tabu search and GRASP for the maximum diversity problem Abraham Duarte.V. All rights reserved. Keywords: Global optimization; Metaheuristics; Tabu search 1. Introduction number of MDP applications in dif- ferent contexts, such as ecological, medical or social sciences
Level Set-based Topological Shape Optimization of Nonlinear Heat Conduction Problems
Seung-Hyun Ha; Seonho Cho
2008-01-01
A level set-based topological shape optimization method is developed for nonlinear heat conduction problems. While minimizing the objective function of instantaneous thermal compliance and satisfying the constraint of allowable volume, solution of the Hamilton-Jacobi equation leads the initial boundary to an optimal one according to the normal velocity field determined from the descent direction of the Lagrangian. To overcome the
On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for its
Ralphs, Ted
On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for its University, USA COR@L Technical Report 14T-004 #12;On the Value Function of a Mixed Integer Linear the value function of a general mixed integer linear optimization prob- lem (MILP). The value function
Optimization of Polling Systems and Dynamic Vehicle Routing Problems on Networks
Bertsimas, Dimitris J.
We consider the problem of optimizing a polling system, i.e., of optimally sequencing a server in a multi-class queueing system with switch-over times in order to minimize a linear objective function of the waiting times. ...
J. Vesterstrom; R. Thomsen
2004-01-01
Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance in several real-world applications. In this paper, we evaluate the performance of DE, PSO, and EAs regarding their general applicability as numerical optimization
ON INTERIOR{POINT NEWTON ALGORITHMS FOR DISCRETIZED OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS
Vicente, Luís Nunes
ON INTERIOR{POINT NEWTON ALGORITHMS FOR DISCRETIZED OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS in detail. We derive an a ne{scaling and two primal{dual interior{point Newton algorithms by applying, in an interior{point way, Newton's method to equivalent forms of the rst{order optimality conditions. Under
Optimal control problem on insect pest populations Bedr'Eddine AINSEBA1
Milner, Fabio Augusto
Optimal control problem on insect pest populations Bedr'Eddine AINSEBA1 , Fabio MILNER2 , Delphine a model of insect infestation of grape vines and consi- der the optimal control of the pest through developed to control this pest, e.g. insecticides, insect growth regulators, and mating disruption [6, 7
Bobrow, James E.
A Fast Sequential Linear Quadratic Algorithm for Solving Unconstrained Nonlinear Optimal Control control problem using sequence of linear quadratic subproblems. Each subproblem is solved efficiently an efficient algorithm for its solution. This algorithm is the well-known Linear Quadratic optimal control
Smoothers for Optimization Problems Eyal Arian \\Lambda and Shlomo Ta'asan y
. Kuruvila and M. D. Salas,[3, 4], which uses a few coarse grids for the optimization process where discretizaÂ tion schemes and a nonÂlinear optimal shape design problem using a bodyÂfitted grid. Results
1. POPs (Polynomial Optimization Problems) 2. Rough sketch of SOS and SDP relaxations of POPs
Kojima, Masakazu
#12;Outline 1. POPs (Polynomial Optimization Problems) 2. Rough sketch of SOS and SDP relaxations of POPs 3. Exploiting structured sparsity --- unconstrained case 4. Exploiting structured sparsity --- constrained case 5. Numerical results 6. Concluding remarks #12;Outline 1. POPs (Polynomial Optimization
Graph-Theoretic Techniques in D-Optimal Design Problems Kashinath Chatterjee Giri Narasimhan y
Narasimhan, Giri
Graph-Theoretic Techniques in D-Optimal Design Problems Kashinath Chatterjee #3; Giri Narasimhan y the number of factors is three or more. Mukerjee, Chatterjee and Sen (1986) and Kra#11;t (1988) showed) considered optimality results on almost saturated main-e#11;ect plans. Chatterjee and Mukerjee (1993
The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots
Minnesota, University of
The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots of Minnesota Minneapolis, MN 55455 Email: {hjmin|npapas}@cs.umn.edu 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
Toader, Anca-Maria
Shape and Topology Optimization for Periodic Problems Part I: The shape and the topological Optimization of Microstructures Â· Shape Derivative Â· Topological Derivative Â· Periodic Homogeniza- tion://cmaf.ptmat.fc.ul.pt/preprints/preprints.html Abstract In the present paper we deduce formulae for the shape and topological derivatives for elliptic
Inverse Problems, Design and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010
Walker, D. Greg
Inverse Problems, Design and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010. Jorge Mechanical Engineering Institute Federal University of Itajub´a Itajub´a, MG, Brazil ariosto and Optimization Symposium Jo~ao Pessoa, Brazil, August 25-27, 2010 ## # # Thermocouples Heat source x y z Figure 1
UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data
Niklaus Eggenberg; Matteo Salani; Michel Bierlaire
2008-01-01
Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the general
Yulong Shi; Sanyou Zeng; Bo Xiao; Yang Yang; Song Gao
This paper proposes an evolutionary algorithm with lower-dimensional-search crossover for constrained engineering optimization\\u000a problems. Crossover operator of the algorithm searches a lower dimensional space determined by the parent points. It is favorable\\u000a to enhance the performance of the algorithm. The algorithm has been used to solve 4 engineering optimization problems with\\u000a constraints. The results show the performance of the proposed
A dual method for optimal control problems with initial and final boundary constraints.
NASA Technical Reports Server (NTRS)
Pironneau, O.; Polak, E.
1973-01-01
This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.
On the application of deterministic optimization methods to stochastic control problems.
NASA Technical Reports Server (NTRS)
Kramer, L. C.; Athans, M.
1972-01-01
A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.
Lagrangian support vector regression via unconstrained convex minimization.
Balasundaram, S; Gupta, Deepak; Kapil
2014-03-01
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
Optimality conditions for multidimensional control problems with polyconvex gradient restrictions
Leipzig, Universität
image processing, 05) thus proving considerable practical importance. 01) Compare [ Ginsburg/Ioffe 96 of the problem is required, as well as [ Ioffe/Tichomirov 79 ] , pp. 201 ff. 02) [ Andrejewa/Kl¨otzler 84a
Optimization technique for problems with an inequality constraint
NASA Technical Reports Server (NTRS)
Russell, K. J.
1972-01-01
General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.
On Some Quadratic Optimization Problems Arising in Computer Vision
Gallier, Jean
, maximize z Az + z b + b z subject to z z = 1, z Cn . Problem 2. If A is a real n Ã? n symmetric matrix and b R is any vector, maximize x Ax + 2x b subject to x x = 1, x Rn . First, we show that Problem 1 the critical points (x, ) of the Lagrangian L(x, ) = x Ax + 2x b - (x x - 1), such that i, for all
Analysis and formulation of a class of complex dynamic optimization problems
NASA Astrophysics Data System (ADS)
Kameswaran, Shivakumar
The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs. The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits. The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization. As an effort to extend the applicability of the direct 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.)
Variational stability of optimal control problems involving subdifferential operators
Tolstonogov, Aleksandr A [Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk (Russian Federation)
2011-04-30
This paper is concerned with the problem of minimizing an integral functional with control-nonconvex integrand over the class of solutions of a control system in a Hilbert space subject to a control constraint given by a phase-dependent multivalued map with closed nonconvex values. The integrand, the subdifferential operators, the perturbation term, the initial conditions and the control constraint all depend on a parameter. Along with this problem, the paper considers the problem of minimizing an integral functional with control-convexified integrand over the class of solutions of the original system, but now subject to a convexified control constraint. By a solution of a control system we mean a 'trajectory-control' pair. For each value of the parameter, the convexified problem is shown to have a solution, which is the limit of a minimizing sequence of the original problem, and the minimal value of the functional with the convexified integrand is a continuous function of the parameter. This property is commonly referred to as the variational stability of a minimization problem. An example of a control parabolic system with hysteresis and diffusion effects is considered. Bibliography: 24 titles.
Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.
The number of convex permutominoes
Paolo Boldi; Violetta Lonati; Roberto Radicioni; Massimo Santini
2008-01-01
Permutominoes are polyominoes defined by suitable pairs of p ermutations. In this paper we provide a formula to count the number of convex permutominoes of given perimeter. To this aim we define the transform of a generic pair of permutations, we c haracterize the transform of any pair defining a convex permutomino, and we solve the counting prob lem in
DISCIPLINED CONVEX PROGRAMMING A DISSERTATION
unifies and generalizes least squares (LS), linear programming (LP), and quadratic programming (QP principles of convex analysis, and inspired by the practices of experts who regularly study and apply convex privilege to be under your tutelage. Your knowledge is boundless, your compassion for your students
Optimal anisotropic three-phase conducting composites: Plane problem
Andrej Cherkaev; and Yuan Zhang
2011-05-22
The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed volume fractions and that the conductivity of one of the materials is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to multiphase structures, it is derived using the technique of {\\em localized polyconvexity} that is a combination of Translation method and additional inequalities on the fields in the materials; similar technique was used by Nesi (1995) and Cherkaev (2009) for isotropic multiphase composites. This paper expands the bounds to the anisotropic composites. The lower bound of conductivity (G-closure) is a piece-wise analytic function of eigenvalues of $K_*$, that depends only on conductivities of components and their volume fractions. Also, we find optimal microstructures that realize the bounds, developing the technique suggested earlier by Albin Cherkaev and Nesi (2007) and Cherkaev (2009). The optimal microstructures are laminates of some rank for all regions. The found structures match the bounds in all but one region of parameters; we discuss the reason for the gap and numerically estimate it.
Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.
Alternative methods for calculating sensitivity of optimized designs to problem parameters
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.; Cai, H. D.
1987-01-01
Optimum sensitivity is defined as the derivative of the optimum design with respect to some problem parameter, P. The problem parameter is usually fixed during optimization, but may be changed later. Thus, optimum sensitivity is used to estimate the effect of changes in loads, materials or constraint bounds on the design without expensive re-optimization. Here, the general topic of optimum sensitivity is discussed, available methods identified, examples given, and the difficulties encountered in calculating this information in nonlinear constrained optimization are identified.
Convex neighborhoods for Lipschitz connections and sprays
E. Minguzzi
2014-11-28
We establish that over a C^{2,1} manifold the exponential map of any Lipschitz connection or spray determines a local Lipeomophism and that, furthermore, reversible convex normal neighborhoods do exist. To that end we use the method of Picard-Lindelof approximation to prove the strong differentiability of the exponential map at the origin and hence a version of Gauss' Lemma which does not require the differentiability of the exponential map. Contrary to naive differential degree counting, the distance functions are shown to gain one degree and hence to be C^{1,1}. As an application to mathematical relativity, it is argued that the mentioned differentiability conditions can be considered the optimal ones to preserve most results of causality theory. This theory is also shown to be generalizable to the Finsler spacetime case. In particular, we prove that the local Lorentzian(-Finsler) length maximization property of causal geodesics in the class of absolutely continuous causal curves holds already for C^{1,1} spacetime metrics. Finally, we study the local existence of convex functions and show that arbitrarily small globally hyperbolic convex normal neighborhoods do exist.
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
NASA Astrophysics Data System (ADS)
Ghosh, Pradipto
The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development 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.
Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem
Jiang, Mingfeng; Jiang, Shanshan; Zhu, Lingyan; Wang, Yaming; Huang, Wenqing; Zhang, Heng
2013-01-01
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
On conjugacy of convex billiards
Kaloshin, Vadim
2012-01-01
Given a strictly convex domain $\\Omega$ in $\\R^2$, there is a natural way to define a billiard map in it: a rectilinear path hitting the boundary reflects so that the angle of reflection is equal to the angle of incidence. In this paper we answer a relatively old question of Guillemin. We show that if two billiard maps are $C^{1,\\alpha}$-conjugate near the boundary, for some $\\alpha > 1/2$, then the corresponding domains are similar, i.e. they can be obtained one from the other by a rescaling and an isometry. As an application, we prove a conditional version of Birkhoff conjecture on the integrability of planar billiards and show that the original conjecture is equivalent to what we call an "Extension problem". Quite interestingly, our result and a positive solution to this extension problem would provide an answer to a closely related question in spectral theory: if the marked length spectra of two domains are the same, is it true that they are isometric?
Lecture for Week 12 (Secs. 5.5 and 5.7) Optimization Problems
Fulling, Stephen
Lecture for Week 12 (Secs. 5.5 and 5.7) Optimization Problems and Antiderivatives 1 #12;We are concerned this week with finding the maximum and minimum values of a function in practical problems and smallest. 8 #12;Example Your dream house will be built on a rectangular lot. Along the side facing
Tracking and Optimal Control Problems in Human Head/Eye Coordination
Ghosh, Bijoy K.
Tracking and Optimal Control Problems in Human Head/Eye Coordination Indika Wijayasinghe1, Eugenio a dynamic model of the head and eye, the eye movement is modeled as a tracking control problem, where the tracking signal depends on the head movement trajectory. The torques required for the head and eye
William F. Eddy; Audris Mockus
1995-01-01
We consider visualization as a decision optimization tool in problems where the model and\\/or the objectives are not well defined. We investigate four specificproblems representing different degrees of determination. The first problem concerns a smooth dynamic representation of data collected at fixed locations. In the example we want to minimize the deviations from a desired temperature over space and time.
Neuro-fuzzy Learning of Strategies for Optimal Control Problems Kaivan Kamali1
Neuro-fuzzy Learning of Strategies for Optimal Control Problems Kaivan Kamali1 , Lijun Jiang2 of neuro-fuzzy systems which yields reusable knowledge in the form of fuzzy if-then rules. Ex- perimental-then rules acquired by training a neuro-fuzzy system can solve similar weight selection problems. 1
An Iterative Solution to the Optimal Premium-Class Routing Problem
Nahrstedt, Klara
1 An Iterative Solution to the Optimal Premium-Class Routing Problem Jun Wang, King-Shan Lui, Li routes for the premium-class traffic such that (1) it works correctly in the context of hop that the negative influences imposed by the premium traffic onto the best-effort traffic are minimized. This problem
Continuous-Time Portfolio Optimization Problem with Transaction Costs: An Option Pricing Approach
Ciocan-Fontanine, Ionut
as a combination of buy-and-hold portfolio problems and optimization problems. In order to solve each buy- and-hold at Tsinghua University as a senior visiting scholar from July to December in 2009, and was a Givens research
The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach
El Asri, Brahim Hamadene, Said
2009-10-15
In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.
Ernesto E. Prudencio; Richard H. Byrd; Xiao-chuan Cai
2006-01-01
Optimization problems constrained by nonlinear partial difierential equations have been the focus of intense research in scientiflc computing lately. Current methods for the parallel numerical solution of such problems involve sequential quadratic programming (SQP), with either reduced or full space approaches. In this paper we propose and investigate a class of parallel full space SQP Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithms. In LNKSz,
Ant Colony Optimization Algorithms with Local Search for the Dynamic Vehicle Routing Problem
Andrew Runka
Abstract This report demonstrates the use of eective,local search to im- prove the performance of simple Ant Colony Optimization (ACO) algorithms as applied to an extension of the Vehicle Routing Problem (VRP) known as the Dynamic Vehicle Routing Problem (DVRP). The static VRP presents all orders a priori, however the DVRP requires scheduling to begin without a complete knowledge of
Optimizing the Slab Yard Planning and Crane Scheduling Problem using a Two-Stage Approach
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
I. Voutchkov; A. J. Keane; A. Bhaskar; Tor M. Olsen
2005-01-01
The solution of combinatorial optimization problems usually involves the consideration of many possible design configurations. This often makes such approaches computationally expensive, especially when dealing with complex finite element models. Here a surrogate model is proposed that can be used to reduce substantially the computational expense of sequential combinatorial finite element problems. The model is illustrated by application to a
Synchronization-Aware and Algorithm-Efficient Chance Constrained Optimal Power Flow
Bent, Russell; Chertkov, Michael
2013-01-01
One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as well as inherent uncertainties about future demand for power and available generation. In this paper we develop convex formulations to appropriately model crucial classes of nonlinearities and stochastic effects. We focus on solving a nonlinear optimal power flow (OPF) problem that includes loss of synchrony constraints and models wind-farm caused fluctuations. In particular, we develop (a) a convex formulation of the deterministic phase-difference nonlinear Optimum Power Flow (OPF) problem; and (b) a probabilistic chance constrained OPF for angular stability, thermal overloads and generation limits that is computationally tractable.
Optimal Control by Multipoles in the Hele-Shaw Problem
NASA Astrophysics Data System (ADS)
Lokutsievskiy, Lev; Runge, Vincent
2015-06-01
The two-dimensional Hele-Shaw problem for a fluid spot with free boundary can be solved using the Polubarinova-Galin equation. The main condition of its applicability is the smoothness of the spot boundary. In the sink-case, this problem is not well-posed and the boundary loses smoothness within finite time—the only exception being the disk centred on the sink. An extensive literature deals with the study of the Hele-Shaw problem with non-smooth boundary or with surface tension, but the problem remains open. In our work, we propose to study this flow from a control point of view, by introducing an analogue of multipoles (term taken from the theory of electromagnetic fields). This allows us to control the shape of the spot and to avoid non-smoothness phenomenon on its border. For any polynomial contours, we demonstrate how all the fluid can be extracted, while the border remains smooth until the very end. We find, in particular, sufficient conditions for controllability and a link between Richardson's moments and Polubarinova-Galin equation.
Intrinsic methods for optimization problems Department of Mathematical Sciences
Topsøe, Flemming
of Copenhagen Universitetsparken 5 DK-2100 Copenhagen, Denmark Email: topsoe@math.ku.dk Abstract-- General entropy distributions and the calculation of information projections. Problems from other areas may also probability distributions on a discrete alphabet, A, for which the mean energy, E, is prescribed. Using x
Robust optimal control for a consumption-investment problem
Schied, Alexander
give an explicit PDE characterization for the solution of the problem of maximizing the utility of both of a risky asset, whose volatility and long-term trend are driven by an external stochastic factor process Forschungsgemeinschaft through the SFB 649 "Economic Risk". AMS 2000 subject classification: 91B28, 49L20, 90C47, 60H10
On copositive programming and standard quadratic optimization problems
Immanuel M. Bomze; Mirjam Dür; Etienne de Klerk; Cornelis Roos; Arie J. Quist; Tamás Terlaky
2000-01-01
A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FFT whereF is some non-negative matrix). The dual of this
Global Optimality Conditions for a Dynamic Blocking Problem
Bressan, Alberto
], these problems were originally motivated by the control of wild fires or the spatial spreading of a contaminating agent. At each time t 0, we denote by R(t) IR2 the region burned by the fire. In absence of control) whenever t1 fire
Algorithmic and Domain Centralization in Distributed Constraint Optimization Problems
-Based Runtime, which takes both communication costs and local computation time into account. We then explore is in some cases a better indicator of solution difficulty than the number of agents in a problem. #12-based systems is an inspiration. I thank Roger Mailler for helpfully providing his implemen- tation of Opt
Applications of Euclidean Geometry to Various Optimization problems
Gallier, Jean
to determine the orbit of the asteroid C#19;eres, and he published a paper about it in 1810 after the discovery of the asteroid Pallas. Incidentally, it is in that same paper that Gaussian elimination using pivots of the asteroid Pallas. #12; 12.1. APPLICATIONS TO LEAST SQUARES PROBLEMS 475 As a concrete illustration, suppose
A numerical study of hybrid optimization methods for the molecular conformation problems
Meza, J.C.; Martinez, M.L.
1993-05-01
An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules depends on the accurate determination of their three-dimensional structure or conformation. Under the assumption that molecules will settle into a configuration for which their energy is at a minimum, this design problem can be formulated as a global optimization problem. The solution of the molecular conformation problem can then be obtained, at least in principle, through any number of optimization algorithms. Unfortunately, it can easily be shown that there exist a large number of local minima for most molecules which makes this an extremely difficult problem for any standard optimization method. In this study, we present results for various optimization algorithms applied to a molecular conformation problem. We include results for genetic algorithms, simulated annealing, direct search methods, and several gradient methods. The major result of this study is that none of these standard methods can be used in isolation to efficiently generate minimum energy configurations. We propose instead several hybrid methods that combine properties of several local optimization algorithms. These hybrid methods have yielded better results on representative test problems than single methods.
Fowler, John Welsh
1986-01-01
of possible tours gets large very quick (as N increases) can make this algorithm computationally expensive for relatively small problems. Users of the NETOPT system should be warned that executing problems with more than ten nodes can result in very...THE DEVELOPMENT OF AN INTERACTIVE MICROCOMPUTER-BASED SYSTEM TO ANALYZE LINEAR NETWORK OPTIMIZATION PROBLEMS A Thesis by JOHN WELSH FOWLER Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirements...
Finite element solution of optimal control problems with state-control inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1992-01-01
It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.
An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem
Zne-jung Lee; Chou-yuan Lee; Shun-feng Su
2002-01-01
In this paper, an immunity-based ant colony optimization (ACO) algorithm for solving weapon–target assignment (WTA) problems is proposed. The WTA problem, known as a NP-complete problem, is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force assets. The general idea of the proposed algorithm is to combine the advantages of
Active Batch Selection via Convex Relaxations with Guaranteed Solution Bounds.
Chakraborty, Shayok; Balasubramanian, Vineeth; Sun, Qian; Panchanathan, Sethuraman; Ye, Jieping
2015-10-01
Active learning techniques have gained popularity to reduce human effort in labeling data instances for inducing a classifier. When faced with large amounts of unlabeled data, such algorithms automatically identify the exemplar instances for manual annotation. More recently, there have been attempts towards a batch mode form of active learning, where a batch of data points is simultaneously selected from an unlabeled set. In this paper, we propose two novel batch mode active learning (BMAL) algorithms: BatchRank and BatchRand. We first formulate the batch selection task as an NP-hard optimization problem; we then propose two convex relaxations, one based on linear programming and the other based on semi-definite programming to solve the batch selection problem. Finally, a deterministic bound is derived on the solution quality for the first relaxation and a probabilistic bound for the second. To the best of our knowledge, this is the first research effort to derive mathematical guarantees on the solution quality of the BMAL problem. Our extensive empirical studies on 15 binary, multi-class and multi-label challenging datasets corroborate that the proposed algorithms perform at par with the state-of-the-art techniques, deliver high quality solutions and are robust to real-world issues like label noise and class imbalance. PMID:26353181
Problems of optimal choice on posets and generalizations of acyclic colourings
Garrod, Bryn James
an optimal strategy for the remaining candidates and r? 1 choices. They found an iterative method to calculate the limits ur = lim n?? t(n, r) n , 12 1. THE CLASSICAL SECRETARY PROBLEM showed that the first few values of ur are e?1, e? 3 2 , e? 47 24 and e... the subject of Ferguson’s history of the problem [26]), but the problem was popularized by Martin Gardner [32, 33] in his Scientific American column in February 1960, as the game goo- gol. The problem itself is simple to state, and its ‘secretary problem...
Data-based Construction of Convex Region Surrogate (CRS) Models
Grossmann, Ignacio E.
University Arul Sundaramoorthy, Jose M. Pinto Praxair Inc., Business and Supply Chain Optimization R computationally efficient and accurate process models. Supply Chain ManagementPlanning and Scheduling 0 24 48 72Data-based Construction of Convex Region Surrogate (CRS) Models Qi Zhang, Ignacio E. Grossmann
NASA Astrophysics Data System (ADS)
Chu, J. G.; Zhang, C.; Fu, G. T.; Li, Y.; Zhou, H. C.
2015-04-01
This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce the computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed problem decomposition dramatically reduces the computational demands required for attaining high quality approximations of optimal tradeoff relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed problem decomposition and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform problem decomposition when solving the complex multi-objective reservoir operation problems.
The Sizing and Optimization Language, (SOL): Computer language for design problems
NASA Technical Reports Server (NTRS)
Lucas, Stephen H.; Scotti, Stephen J.
1988-01-01
The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.
NASA Astrophysics Data System (ADS)
Zamirian, M.; Kamyad, A. V.; Farahi, M. H.
2009-09-01
In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.
The minimum cost optimal power flow problem solved via the restart homotopy continuation method
Ponpajah, R.A.; Galiana, F.D.
1989-02-01
The potential of the continuation method to solve the minimum cost optimal power (OPF) flow problem is assessed. Initially, the complete OPF problem is simplified by creating a sub-problem in which limits on functional variables are ignored. The restart homotopy continuation algorithm developed solves the sub-problem by manipulating the control variables to satisfy the optimality conditions of a family of relaxed sub-problems which converge to the desired solution. Particular features of this minimum cost problem are exploited to make the algorithm very efficient. If the solution to the sub-problem does not yield functional violations, then it becomes the solution to the complete OPF problem. However, if functional violations prevail, a new sub-problem is created by taking into consideration the functional violations, such that the newly created sub-problem maintains the same basic structure as its predecessor. This enables the restart homotopy continuation algorithm to be reapplied to solve the newly created sub-problem. The process is repeated until no functional violations prevail.
Optimizing Constrained Single Period Problem under Random Fuzzy Demand
NASA Astrophysics Data System (ADS)
Taleizadeh, Ata Allah; Shavandi, Hassan; Riazi, Afshin
2008-09-01
In this paper, we consider the multi-product multi-constraint newsboy problem with random fuzzy demands and total discount. The demand of the products is often stochastic in the real word but the estimation of the parameters of distribution function may be done by fuzzy manner. So an appropriate option to modeling the demand of products is using the random fuzzy variable. The objective function of proposed model is to maximize the expected profit of newsboy. We consider the constraints such as warehouse space and restriction on quantity order for products, and restriction on budget. We also consider the batch size for products order. Finally we introduce a random fuzzy multi-product multi-constraint newsboy problem (RFM-PM-CNP) and it is changed to a multi-objective mixed integer nonlinear programming model. Furthermore, a hybrid intelligent algorithm based on genetic algorithm, Pareto and TOPSIS is presented for the developed model. Finally an illustrative example is presented to show the performance of the developed model and algorithm.
Three-dimensional strong convexity and visibility
NASA Astrophysics Data System (ADS)
Fink, Eugene; Wood, Derick
1995-08-01
We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties of standard convex sets: (1) Every two points of a convex set are visible to each other. (2) The intersection of convex sets is a convex set. (3) For every point in the boundary of a convex set, there exists a supporting plane through this point. (4) A closed convex set in three dimensions is the intersection of all halfspaces that contain it.
NASA Astrophysics Data System (ADS)
Tang, Yuchao
2015-03-01
Computed tomography (CT) image reconstruction problems can be solved by finding the minimization of a suitable objective function. The first-order methods for image reconstruction in CT have been popularized in recent years. These methods are interesting because they need only the first derivative information of the objective function and can solve non-smooth regularization functions. In this paper, we consider a constrained optimization problem which often appeared in the CT image reconstruction problems. For the unconstrained case, it has been studied recently. We dedicate to propose an efficient algorithm to solve the constrained optimization problem. Numerical experiments to image reconstruction benchmark problem show that the proposed algorithms can produce better reconstructed images in signal-to-noise than the original algorithm and other state-of-the-art methods.
NASA Technical Reports Server (NTRS)
Tapia, R. A.; Vanrooy, D. L.
1976-01-01
A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.
Direct SQP-methods for solving optimal control problems with delays
Goellmann, L.; Bueskens, C.; Maurer, H.
1994-12-31
The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method for retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.
Approximate Euclidean Shortest Paths amid Convex Obstacles Pankaj K. Agarwal R. Sharathkumar Hai Yu
Agarwal, Pankaj K.
Approximate Euclidean Shortest Paths amid Convex Obstacles Pankaj K. Agarwal R. Sharathkumar Hai Yu and data structures for the approximate Euclidean shortest path problem amid a set P of k convex obstacles for computing the exact Euclidean shortest path between two points amid polygonal obstacles. In three dimensions
Cost-Optimal Operation of Energy Storage Units: Benefits of a Problem-Specific Approach
Siemer, Lars; Kleinhans, David
2015-01-01
The integration of large shares of electricity produced by non-dispatchable Renewable Energy Sources (RES) leads to an increasingly volatile energy generation side, with temporary local overproduction. The application of energy storage units has the potential to use this excess electricity from RES efficiently and to prevent curtailment. The objective of this work is to calculate cost-optimal charging strategies for energy storage units used as buffers. For this purpose, a new mathematical optimization method is presented that is applicable to general storage-related problems. Due to a tremendous gain in efficiency of this method compared with standard solvers and proven optimality, calculations of complex problems as well as a high-resolution sensitivity analysis of multiple system combinations are feasible within a very short time. As an example technology, Power-to-Heat converters used in combination with thermal storage units are investigated in detail and optimal system configurations, including storage ...
Optimization of location routing inventory problem with transshipment
NASA Astrophysics Data System (ADS)
Ghani, Nor Edayu Abd; Shariff, S. Sarifah Radiah; Zahari, Siti Meriam
2015-05-01
Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.
Erem, Burak; van Dam, Peter M.; Brooks, Dana H.
2014-01-01
Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a non-convex, non-linear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second. PMID:24710159
Min-Geun Kim; Seung-Hyun Ha; Seonho Cho
2009-01-01
A level set-based topological shape-optimization method is developed to relieve the well-known convergence difficulty in nonlinear heat-conduction problems. While minimizing the objective function of instantaneous thermal compliance and satisfying the constraint of allowable volume, the solution of the Hamilton–Jacobi equation leads the initial implicit boundary to an optimal one according to the normal velocity determined from the descent direction of
Ant colony optimization technique for the sequence-dependent flowshop scheduling problem
Mohammad Mirabi
2011-01-01
In the real world, production scheduling systems, usually optimal job scheduling, requires an explicit consideration of sequence-dependent\\u000a setup times. One of the most important scheduling criteria in practical systems is makespan. In this paper, the author presents\\u000a an ant colony optimization (ACO) algorithm for the sequence-dependent permutation flowshop scheduling problem. The proposed\\u000a ACO algorithm benefits from a new approach for
Vortex generator design for aircraft inlet distortion as a numerical optimization problem
NASA Technical Reports Server (NTRS)
Anderson, Bernhard H.; Levy, Ralph
1991-01-01
Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.
Wagner F. Sacco; Marcelo D. Machado; Cláudio M. N. A. Pereira; Roberto Schirru
2004-01-01
This article extends previous efforts on genetic algorithms (GAs) applied to a core design optimization problem. We introduce the application of a new Niching Genetic Algorithm (NGA) to this problem and compare its performance to these previous works. The optimization problem consists in adjusting several reactor cell parameters, such as dimensions, enrichment and materials, in order to minimize the average
Pedram, Massoud
of near-continuous library allows one to model the problem as a mathematical optimization problem-continuous size inverter libraries. It is demonstrated that because of neglecting short-circuit current, previous. The paper describes how the problem of low-power fanout optimization can be reduced to inverter chain
Optimizing the Steel Plate Storage Yard Crane Scheduling Problem Using a Two Stage Planning Petersens Plads, 2800 Lyngby, Denmark adh@imm.dtu.dk This paper presents the Steel Plate Storage Yard Crane The Steel Plate Storage Yard Crane Scheduling Problem is a difficult optimization problem, combining
NASA Astrophysics Data System (ADS)
Igeta, Hideki; Hasegawa, Mikio
Chaotic dynamics have been effectively applied to improve various heuristic algorithms for combinatorial optimization problems in many studies. Currently, the most used chaotic optimization scheme is to drive heuristic solution search algorithms applicable to large-scale problems by chaotic neurodynamics including the tabu effect of the tabu search. Alternatively, meta-heuristic algorithms are used for combinatorial optimization by combining a neighboring solution search algorithm, such as tabu, gradient, or other search method, with a global search algorithm, such as genetic algorithms (GA), ant colony optimization (ACO), or others. In these hybrid approaches, the ACO has effectively optimized the solution of many benchmark problems in the quadratic assignment problem library. In this paper, we propose a novel hybrid method that combines the effective chaotic search algorithm that has better performance than the tabu search and global search algorithms such as ACO and GA. Our results show that the proposed chaotic hybrid algorithm has better performance than the conventional chaotic search and conventional hybrid algorithms. In addition, we show that chaotic search algorithm combined with ACO has better performance than when combined with GA.
Convex polytopes and quantum separability
Holik, F.; Plastino, A.
2011-12-15
We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.
Approximate dynamic programming recurrence relations for a hybrid optimal control problem
NASA Astrophysics Data System (ADS)
Lu, W.; Ferrari, S.; Fierro, R.; Wettergren, T. A.
2012-06-01
This paper presents a hybrid approximate dynamic programming (ADP) method for a hybrid dynamic system (HDS) optimal control problem, that occurs in many complex unmanned systems which are implemented via a hybrid architecture, regarding robot modes or the complex environment. The HDS considered in this paper is characterized by a well-known three-layer hybrid framework, which includes a discrete event controller layer, a discrete-continuous interface layer, and a continuous state layer. The hybrid optimal control problem (HOCP) is to nd the optimal discrete event decisions and the optimal continuous controls subject to a deterministic minimization of a scalar function regarding the system state and control over time. Due to the uncertainty of environment and complexity of the HOCP, the cost-to-go cannot be evaluated before the HDS explores the entire system state space; as a result, the optimal control, neither continuous nor discrete, is not available ahead of time. Therefore, ADP is adopted to learn the optimal control while the HDS is exploring the environment, because of the online advantage of ADP method. Furthermore, ADP can break the curses of dimensionality which other optimizing methods, such as dynamic programming (DP) and Markov decision process (MDP), are facing due to the high dimensions of HOCP.