Introduction to Global Optimization (Nonconvex Optimization and its Applications)

Reiner Horst; Panos M. Pardalos; Nguyen Van Thoai

ISBN 10: 0792365747 / ISBN 13: 9780792365747

Verlag: Springer, 2000

Beschreibung

Hardcover, second edition, xiv + 353 pages, NOT ex-library. A gentle crease in side margin of a portion of leaves; faint grubby handling marks on page edges externally. Interior is clean and bright throughout, with unmarked text, free of inscriptions and stamps, firmly bound. Boards show gentle handling wear, limited scuffing. Published without a dust jacket. -- Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Global optimization is concerned with the computation and characterization of global optima of nonlinear functions. Global optimization problems are widespread in the mathematical modeling of real world systems for a very broad range of applications. During the past three decades many new theoretical, algorithmic, and computational contributions have helped to solve globally multi-extreme problems arising from important practical applications. Introduction to Global Optimization is the first comprehensive textbook that covers the fundamentals in global optimization. The second edition includes algorithms, applications, and complexity results for quadratic programming, concave minimization, DC and Lipshitz problems, decomposition algorithms for nonconvex optimization, and nonlinear network flow problems. Each chapter contains illustrative examples and ends with carefully selected exercises, which are designed to help the student to get a grasp of the material and enhance their knowledge of global optimization methods. Audience: This textbook is addressed not only to students of mathematical programming, but to all scientists in various disciplines who need global optimization methods to model and solve problems. -- Contents: Fundamental Results; Convex Sets and Functions; General Properties of Optimization Problems; Convex Envelope; Kuhn-Tucker Conditions; Second Order Optimality Conditions; Duality in Nonlinear Programming; Complexity Issues; Quadratic Programming; Quadratic Integer Programming; Linear Complementarity Problem; Complexity of Quadratic Optimization; Enumerative Methods; Separation and Interpolation; General Concave Minimization; Applications; Basic Operations; Cutting Plane Algorithms; Outer Approximation Algorithms; Inner Approximation; Branch and Bound Algorithms; Simplicial Branch and Bound Approach; D.C. Programming; Space of D.C. Functions; Some Additional Applications; Optimality Conditions; Canonical D.C. Program; Simplicial Branch and Bound Algorithm; Prismatic Algorithm; Lipschitz Optimization; Lipschitz Functions; Lipschitz Optimization Problems; Lower Bounds; Branch and Bound Algorithms; Implementation; Global Optimization on Networks; Some MCCFP Models and its Complexity; Solution Methods; Decomposition Algorithms; Variable Decomposition: Conical Algorithm; Variable Decomposition: Outer Approximation; Constraint Decomposition: Conical Algorithm; Constraint Decomposition: Cutting Algorithm; Solutions; Selected References; Index. Bestandsnummer des Verkäufers 005179

Bibliografische Details

Titel: Introduction to Global Optimization (...

Verlag: Springer

Erscheinungsdatum: 2000

Einband: Hardcover

Zustand: Good

Auflage: 2nd Edition

Über diesen Titel

Inhaltsangabe:

In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P.M. Pardalos and N.V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu­ merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di­ verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith­ mic, and computational contributions have helped to solve globally multi­ extreme problems arising from important practical applications.

Críticas:

Comments on the first edition:
`Each chapter contains illlustrative examples and exercises. This excellent book is the first textbook on deterministic global optimization.'
Mathematical Reviews (96g:90001)
`The authors provide a nice selection of homework exercises (with solutions) at an appropriate level and a good mixture of theory, application, and numerical problems throughout the text. The text would be perfect for a course on global optimization.'
Interfaces 28 (1998)
`Overall, this book provides an excellent introduction to the fascinating field of global optimization. The authors have used their extensive knowledge of and perspective on the field to create a coherent text that is accessible to a large audience that includes both students of mathematical programming and scientists who utilize optimization in their work.'
Journal of Global Optimization 9 (1996)