Handbook of Global Optimization

Handbook of Global Optimization

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.

Author: R. Horst

Publisher: Springer

ISBN: 1461358388

Category: Mathematics

Page: 880

View: 306

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.
Categories: Mathematics

Handbook of Global Optimization

Handbook of Global Optimization

In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published.

Author: Panos M. Pardalos

Publisher: Springer Science & Business Media

ISBN: 9781475753622

Category: Mathematics

Page: 572

View: 356

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.
Categories: Mathematics

Deterministic Global Optimization

Deterministic Global Optimization

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 ...

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

ISBN: 9781475749496

Category: Mathematics

Page: 742

View: 673

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.
Categories: Mathematics

Handbook of Test Problems in Local and Global Optimization

Handbook of Test Problems in Local and Global Optimization

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic ...

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

ISBN: 9781475730401

Category: Technology & Engineering

Page: 442

View: 551

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic separation, and dynamic optimization and optimal control problems.
Categories: Technology & Engineering

Global Optimization

Global Optimization

The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented.

Author: Reiner Horst

Publisher: Springer Science & Business Media

ISBN: 9783662025987

Category: Business & Economics

Page: 696

View: 177

The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years ago would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented. By definition, a multiextremal global optimization problem seeks at least one global minimizer of a real-valued objective function that possesses different local n minimizers. The feasible set of points in IR is usually determined by a system of inequalities. It is well known that in practically all disciplines where mathematical models are used there are many real-world problems which can be formulated as multi extremal global optimization problems.
Categories: Business & Economics

Global Optimization

Global Optimization

Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms.

Author: Leo Liberti

Publisher: Springer Science & Business Media

ISBN: 9780387305288

Category: Mathematics

Page: 428

View: 724

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.
Categories: Mathematics

Introduction to Global Optimization

Introduction to Global Optimization

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).

Author: R. Horst

Publisher: Springer Science & Business Media

ISBN: 0792367561

Category: Computers

Page: 354

View: 747

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
Categories: Computers

Stochastic Adaptive Search for Global Optimization

Stochastic Adaptive Search for Global Optimization

Vavasis, S.A., “Complexity Issues in Global Optimization: A Survey,” in Handbook of Global Optimization, edited by R. Horst, and P.M. Pardalos, Kluwer Academic Publishers, Netherlands, 27-41, 1995. Vinson J.R., and Chou, T-W.

Author: Z.B. Zabinsky

Publisher: Springer Science & Business Media

ISBN: 9781441991829

Category: Mathematics

Page: 224

View: 503

The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo rithms, are gaining in popularity among practitioners and engineers be they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these stochastic methods is not well under stood. In this book, an attempt is made to describe the theoretical prop erties of several stochastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and de velopment of stochastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical anal ysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use stochastic adaptive search methods.
Categories: Mathematics

Integral Global Optimization

Integral Global Optimization

This book treats the subject of global optimization with minimal restrictions on the behavior on the objective functions.

Author: Soo H. Chew

Publisher: Springer

ISBN: 3540187723

Category: Business & Economics

Page: 179

View: 560

This book treats the subject of global optimization with minimal restrictions on the behavior on the objective functions. In particular, optimal conditions were developed for a class of noncontinuous functions characterized by their having level sets that are robust. The integration-based approach contrasts with existing approaches which require some degree of convexity or differentiability of the objective function. Some computational results on a personal computer are presented.
Categories: Business & Economics

Abstract Convexity and Global Optimization

Abstract Convexity and Global Optimization

This book consists of two parts.

Author: Alexander M. Rubinov

Publisher: Springer Science & Business Media

ISBN: 079236323X

Category: Mathematics

Page: 490

View: 158

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.
Categories: Mathematics

Convex Analysis and Global Optimization

Convex Analysis and Global Optimization

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.

Author: Hoang Tuy

Publisher: Springer

ISBN: 9783319314846

Category: Mathematics

Page: 505

View: 182

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)
Categories: Mathematics

Global Optimization

Global Optimization

Horst , R. and Pardalos , P.M. , Eds . ( 1995 ) Handbook of Global Optimization , Vol . 1. Kluwer Academic Publishers , Dordrecht . 18. Hillier , F. and Lieberman , G.J. ( 2005 ) Introduction to Operations Research . ( 8th Edition . ) ...

Author: Leo Liberti

Publisher: Springer Science & Business Media

ISBN: 0387282602

Category: Business & Economics

Page: 427

View: 984

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.
Categories: Business & Economics

State of the Art in Global Optimization

State of the Art in Global Optimization

Boender, C. G. E., and Romeijn, H. E., “Stochastic methods,” In: Handbook of Global Optimization, R. Horst, P. M. Pardalos, eds., Kluwer, Dordrecht, 1995, pp. 829–869. . L. Breiman, L., and A. Cutler, A., “A deterministic algorithm for ...

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

ISBN: 9781461334378

Category: Mathematics

Page: 654

View: 852

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.
Categories: Mathematics

Handbook of Test Problems in Local and Global Optimization

Handbook of Test Problems in Local and Global Optimization

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic ...

Author: Christodoulos A. Floudas

Publisher: Springer

ISBN: 1475730411

Category: Technology & Engineering

Page: 442

View: 729

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic separation, and dynamic optimization and optimal control problems.
Categories: Technology & Engineering

Deterministic Global Optimization

Deterministic Global Optimization

This book begins with a concentrated introduction into deterministic global optimization and moves forward to present new original results from the authors who are well known experts in the field.

Author: Yaroslav D. Sergeyev

Publisher: Springer

ISBN: 1493971972

Category: Computers

Page: 136

View: 638

This book begins with a concentrated introduction into deterministic global optimization and moves forward to present new original results from the authors who are well known experts in the field. Multiextremal continuous problems that have an unknown structure with Lipschitz objective functions and functions having the first Lipschitz derivatives defined over hyperintervals are examined. A class of algorithms using several Lipschitz constants is introduced which has its origins in the DIRECT (DIviding RECTangles) method. This new class is based on an efficient strategy that is applied for the search domain partitioning. In addition a survey on derivative free methods and methods using the first derivatives is given for both one-dimensional and multi-dimensional cases. Non-smooth and smooth minorants and acceleration techniques that can speed up several classes of global optimization methods with examples of applications and problems arising in numerical testing of global optimization algorithms are discussed. Theoretical considerations are illustrated through engineering applications. Extensive numerical testing of algorithms described in this book stretches the likelihood of establishing a link between mathematicians and practitioners. The authors conclude by describing applications and a generator of random classes of test functions with known local and global minima that is used in more than 40 countries of the world. This title serves as a starting point for students, researchers, engineers, and other professionals in operations research, management science, computer science, engineering, economics, environmental sciences, industrial and applied mathematics to obtain an overview of deterministic global optimization.
Categories: Computers

Continuous Optimization

Continuous Optimization

'Man94] MPV01] MM02] PR02] jPiii95] jPwzo2j RY03] 'Smi02] International Conference on Optimization: Techniques and ... Machine Learning, 49, 291—323 (2002) Pardalos, P., Romeijn, H. (eds): Handbook of Global Optimization, 2, ...

Author: V. Jeyakumar

Publisher: Springer Science & Business Media

ISBN: 9780387267715

Category: Mathematics

Page: 450

View: 508

Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.
Categories: Mathematics

Solving Non standard Packing Problems by Global Optimization and Heuristics

Solving Non standard Packing Problems by Global Optimization and Heuristics

Handbook of Applied Optimization. Oxford University Press, Oxford (2002) Pardalos, P.M., Romeijn, H.E. (eds.): Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands (2002) Parren ̃o, F., Alvarez-Valdes, ...

Author: Giorgio Fasano

Publisher: Springer

ISBN: 9783319050058

Category: Mathematics

Page: 135

View: 889

This book results from a long-term research effort aimed at tackling complex non-standard packing issues which arise in space engineering. The main research objective is to optimize cargo loading and arrangement, in compliance with a set of stringent rules. Complicated geometrical aspects are also taken into account, in addition to balancing conditions based on attitude control specifications. Chapter 1 introduces the class of non-standard packing problems studied. Chapter 2 gives a detailed explanation of a general model for the orthogonal packing of tetris-like items in a convex domain. A number of additional conditions are looked at in depth, including the prefixed orientation of subsets of items, the presence of unusable holes, separation planes and structural elements, relative distance bounds as well as static and dynamic balancing requirements. The relative feasibility sub-problem which is a special case that does not have an optimization criterion is discussed in Chapter 3. This setting can be exploited by introducing an ad hoc objective function, aimed at facilitating the finding of integer-feasible solutions. The third chapter also discusses the issue of tightening the general MIP model by introducing valid inequalities. A MIP-based heuristic approach is developed in Chapter 4, where the basic concept of abstract configuration is presented. Chapter 5 is devoted to experimental results relevant to a real-world application framework. Chapter 6 adopts both extensions of the general MIP model and non-linear formulations to tackle two further non-standard packing issues. The final Chapter 7 presents conclusions and provides insights regarding prospective developments (including non-standard scheduling aspects). Practitioners and researchers interested in advanced optimization model development and solution in the context of logistics, transportation systems, complex structures, manufacturing and electronics will find this book useful. The book can also be used in graduate courses on nonlinear - including global and mixed integer - optimization, as a valuable collection of practically meaningful object packing applications.
Categories: Mathematics

Global Optimization with Non Convex Constraints

Global Optimization with Non Convex Constraints

State of the Art in Global Optimization. Kluwer Academic Publishers, Dordrecht. Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., Gümüs, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., and Schweiger, C.A. (1999). Handbook of ...

Author: Roman G. Strongin

Publisher: Springer Science & Business Media

ISBN: 9781461546771

Category: Mathematics

Page: 704

View: 956

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.
Categories: Mathematics

Global Optimization

Global Optimization

Quadratic Optimization. In: Horst, R. and Pardalos, P.M. (eds.), Handbook of Global Optimization, 217-270, Kluwer, Dordrecht–Boston—London. FORGO, F. (1972), Cutting Plane Methods for Solving Nonconvez Quadratic Problems.

Author: Reiner Horst

Publisher: Springer Science & Business Media

ISBN: 9783662031995

Category: Business & Economics

Page: 730

View: 309

The main contents and character of the monograph did not change with respect to the first edition. However, within most chapters we incorporated quite a number of modifications which take into account the recent development of the field, the very valuable suggestions and comments that we received from numerous colleagues and students as well as our own experience while using the book. Some errors and misprints in the first edition are also corrected. Reiner Horst May 1992 Hoang Tuy PREFACE TO THE FIRST EDITION The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years aga would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented.
Categories: Business & Economics

Stochastic Global Optimization

Stochastic Global Optimization

G. Ostrovski and et all, Flexibility analysis of chemical processes: selected global optimization problems, Optimiz. Eng. 3 (2002), 31–52. P. Pardalos and E. Romeijn, Handbook of global optimization, volume 2, Kluwer: Dodrecht, 2002.

Author: Anatoly Zhigljavsky

Publisher: Springer Science & Business Media

ISBN: 9780387747408

Category: Mathematics

Page: 262

View: 459

This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.
Categories: Mathematics