Global Optimization With Non Convex Constraints

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Global Optimization with Non-Convex Constraints

Roman G. Strongin,Yaroslav D. Sergeyev
Global Optimization with Non Convex Constraints Book PDF

Author : Roman G. Strongin,Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
Page : 717 pages
File Size : 48,6 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.

Introduction to Global Optimization

R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Introduction to Global Optimization Book PDF

Author : R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 47,7 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

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Mohit Tawarmalani,Nikolaos V. Sahinidis
Convexification and Global Optimization in Continuous and Mixed Integer Nonlinear Programming Book PDF

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 55,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Frontiers in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Frontiers in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 43,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302513

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Frontiers in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Stochastic Adaptive Search for Global Optimization

Z.B. Zabinsky
Stochastic Adaptive Search for Global Optimization Book PDF

Author : Z.B. Zabinsky
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 45,5 Mb
Release : 2003-09-30
Category : Computers
ISBN : 140207526X

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Stochastic Adaptive Search for Global Optimization by Z.B. Zabinsky Pdf

The book overviews several stochastic adaptive search methods for global optimization and provides analytical results regarding their performance and complexity. It develops a class of hit-and-run algorithms that are theoretically motivated and do not require fine-tuning of parameters. Several engineering global optimization problems are summarized to demonstrate the kinds of practical problems that are now within reach. Audience: This book is suitable for graduate students, researchers and practitioners in operations research, engineering, and mathematics.

Non-Convex Multi-Objective Optimization

Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas
Non Convex Multi Objective Optimization Book PDF

Author : Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas
Publisher : Springer
Page : 196 pages
File Size : 52,5 Mb
Release : 2017-07-27
Category : Mathematics
ISBN : 9783319610078

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Non-Convex Multi-Objective Optimization by Panos M. Pardalos,Antanas Žilinskas,Julius Žilinskas Pdf

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

Convex Analysis and Global Optimization

Hoang Tuy
Convex Analysis and Global Optimization Book PDF

Author : Hoang Tuy
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 50,6 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.

Global Optimization

Leo Liberti,Nelson Maculan
Global Optimization Book PDF

Author : Leo Liberti,Nelson Maculan
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 47,7 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780387305288

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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.

Handbook of Global Optimization

R. Horst,Panos M. Pardalos
Handbook of Global Optimization Book PDF

Author : R. Horst,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 891 pages
File Size : 53,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461520252

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Handbook of Global Optimization by R. Horst,Panos M. Pardalos Pdf

Global optimization is concerned with the computation and characterization of global optima of nonlinear functions. During the past three decades the field of global optimization has been growing at a rapid pace, and the number of publications on all aspects of global optimization has been increasing steadily. Many applications, as well as new theoretical, algorithmic, and computational contributions have resulted. The Handbook of Global Optimization is the first comprehensive book to cover recent developments in global optimization. Each contribution in the Handbook is essentially expository in nature, but scholarly in its treatment. The chapters cover optimality conditions, complexity results, concave minimization, DC programming, general quadratic programming, nonlinear complementarity, minimax problems, multiplicative programming, Lipschitz optimization, fractional programming, network problems, trajectory methods, homotopy methods, interval methods, and stochastic approaches. The Handbook of Global Optimization is addressed to researchers in mathematical programming, as well as all scientists who use optimization methods to model and solve problems.

Convex Analysis and Global Optimization

Hoang Tuy
Convex Analysis and Global Optimization Book PDF

Author : Hoang Tuy
Publisher : Springer
Page : 505 pages
File Size : 47,5 Mb
Release : 2016-10-17
Category : Mathematics
ISBN : 9783319314846

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Convex Analysis and Global Optimization by Hoang Tuy Pdf

This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints; · Important discussions of decomposition methods for specially structured problems; · A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition. · Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint. From the reviews of the first edition: The book gives a good review of the topic. ...The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.—Mathematical Methods of Operations Research, 49:3 (1999)

State of the Art in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
State of the Art in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 55,8 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.

Abstract Convexity and Global Optimization

Alexander M. Rubinov
Abstract Convexity and Global Optimization Book PDF

Author : Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 40,8 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.

Convex Optimization

Stephen P. Boyd,Lieven Vandenberghe
Convex Optimization Book PDF

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 54,7 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Frontiers in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Frontiers in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 42,8 Mb
Release : 2004
Category : Computers
ISBN : 1402076991

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Frontiers in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. The chapters in this volume focus on recent deterministic methods and stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimization in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Handbook of Global Optimization

Panos M. Pardalos,H. Edwin Romeijn
Handbook of Global Optimization Book PDF

Author : Panos M. Pardalos,H. Edwin Romeijn
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 47,9 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.