Global Optimization

Author : Marco Locatelli,Fabio Schoen
Publisher : SIAM
Page : 439 pages
File Size : 50,8 Mb
Release : 2013-10-16
Category : Mathematics
ISBN : 9781611972672

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Global Optimization by Marco Locatelli,Fabio Schoen Pdf

This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.

Author : Panos M. Pardalos,Judah Ben Rosen
Publisher : Springer
Page : 160 pages
File Size : 46,6 Mb
Release : 1987
Category : Computers
ISBN : UOM:39015015631529

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Constrained Global Optimization by Panos M. Pardalos,Judah Ben Rosen Pdf

Author : Hoang Tuy
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 46,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475728095

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Convex Analysis and Global Optimization by Hoang Tuy Pdf

Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.

Author : R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 44,5 Mb
Release : 2000-12-31
Category : Computers
ISBN : 0792367561

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Introduction to Global Optimization by R. Horst,Panos M. Pardalos,Nguyen Van Thoai Pdf

A textbook for an undergraduate course in mathematical programming for students with a knowledge of elementary real analysis, linear algebra, and classical linear programming (simple techniques). Focuses on the computation and characterization of global optima of nonlinear functions, rather than the locally optimal solutions addressed by most books on optimization. Incorporates the theoretical, algorithmic, and computational advances of the past three decades that help solve globally multi-extreme problems in the mathematical modeling of real world systems. Annotation copyright by Book News, Inc., Portland, OR

Author : Yaroslav D. Sergeyev,Roman G. Strongin,Daniela Lera
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 43,6 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781461480426

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Introduction to Global Optimization Exploiting Space-Filling Curves by Yaroslav D. Sergeyev,Roman G. Strongin,Daniela Lera Pdf

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful . ​

Author : Leo Liberti,Nelson Maculan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 53,9 Mb
Release : 2006-02-21
Category : Business & Economics
ISBN : 0387282602

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Global Optimization by Leo Liberti,Nelson Maculan Pdf

Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms. It discusses existing software packages from which the entire community can learn. The contributors are experts in the discipline of actually getting global optimization to work, and the book provides a source of ideas for people needing to implement global optimization software.

Author : János D. Pintér
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 52,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475725025

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Global Optimization in Action by János D. Pintér Pdf

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s). Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues. Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

Author : Panos M. Pardalos,H. Edwin Romeijn
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 45,5 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781475753622

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Handbook of Global Optimization by Panos M. Pardalos,H. Edwin Romeijn Pdf

In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published. This second volume of the Handbook of Global Optimization is comprised of chapters dealing with modern approaches to global optimization, including different types of heuristics. Topics covered in the handbook include various metaheuristics, such as simulated annealing, genetic algorithms, neural networks, taboo search, shake-and-bake methods, and deformation methods. In addition, the book contains chapters on new exact stochastic and deterministic approaches to continuous and mixed-integer global optimization, such as stochastic adaptive search, two-phase methods, branch-and-bound methods with new relaxation and branching strategies, algorithms based on local optimization, and dynamical search. Finally, the book contains chapters on experimental analysis of algorithms and software, test problems, and applications.

Author : Panos M Pardalos,Athanasios Migdalas,Rainer E Burkard
Publisher : World Scientific
Page : 372 pages
File Size : 41,6 Mb
Release : 2002-04-05
Category : Mathematics
ISBN : 9789814489652

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Combinatorial and Global Optimization by Panos M Pardalos,Athanasios Migdalas,Rainer E Burkard Pdf

Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans–Williamson relaxation of the maximum cut problem, and the Du–Hwang solution of the Gilbert–Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece. Contents:A Forest Exterior Point Algorithm for Assignment Problems (H Achatz et al.)Location/Allocation of Queuing Facilities in Continuous Space Using Minsum and Minimax Criteria (J Brimberg et al.)Algorithms for the Consistency Analysis in Scenario Projects (R Feldmann et al.)Solving Quadratic Knapsack Problems by Reformulation and Tabu Search. Single Constraint Case (F Glover et al.)Global Optimization Using Dynamic Search Trajectories (A A Groenwold & J A Snyman)On Pareto Efficiency. A General Constructive Existence Principle (G Isac)Piecewise Linear Network Flow Problems (D Kim & P M Pardalos)Semidefinite Programming Approaches for MAX-2-SAT and MAX-3-SAT: Computational Perspectives (E de Klerk & J P Warners)Heuristic Solutions of Vehicle Routing Problems in Supply Chain Management (Y Marinakis & A Migdalas)A New Finite Cone Covering Algorithm for Concave Minimization (C Meyer & B Jaumard)Frequency Assignment for Very Large, Sparse Networks (R Murphey)GPS Network Design: An Application of the Simulated Annealing Heuristic Technique (H A Saleh & P J Dare)Normal Branch and Bound Algorithms for General Nonconvex Quadratic Programming (H Tuy)and other papers Readership: Researchers in numerical & computational mathematics, optimization, combinatorics & graph theory, networking and materials engineering. Keywords:Combinatorial Optimization;Global Optimization

Author : Roman G. Strongin,Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
Page : 717 pages
File Size : 54,7 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781461546771

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Global Optimization with Non-Convex Constraints by Roman G. Strongin,Yaroslav D. Sergeyev Pdf

Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model.

Author : Kenneth Price,Rainer M. Storn,Jouni A. Lampinen
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 43,7 Mb
Release : 2006-03-04
Category : Mathematics
ISBN : 9783540313069

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Differential Evolution by Kenneth Price,Rainer M. Storn,Jouni A. Lampinen Pdf

Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables. The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization.

Author : Remigijus Paulavičius,Julius Žilinskas
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 48,8 Mb
Release : 2013-10-09
Category : Business & Economics
ISBN : 9781461490937

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Simplicial Global Optimization by Remigijus Paulavičius,Julius Žilinskas Pdf

Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 47,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334378

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State of the Art in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Page : 741 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475749496

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Deterministic Global Optimization by Christodoulos A. Floudas Pdf

The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.

Author : Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 45,8 Mb
Release : 2000-05-31
Category : Mathematics
ISBN : 079236323X

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Abstract Convexity and Global Optimization by Alexander M. Rubinov Pdf

This book consists of two parts. Firstly, the main notions of abstract convexity and their applications in the study of some classes of functions and sets are presented. Secondly, both theoretical and numerical aspects of global optimization based on abstract convexity are examined. Most of the book does not require knowledge of advanced mathematics. Classical methods of nonconvex mathematical programming, being based on a local approximation, cannot be used to examine and solve many problems of global optimization, and so there is a clear need to develop special global tools for solving these problems. Some of these tools are based on abstract convexity, that is, on the representation of a function of a rather complicated nature as the upper envelope of a set of fairly simple functions. Audience: The book will be of interest to specialists in global optimization, mathematical programming, and convex analysis, as well as engineers using mathematical tools and optimization techniques and specialists in mathematical modelling.