Deterministic Global Optimization: Geometric Branch-and-bound Methods and their

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Deterministic Global Optimization by Daniel Scholz

This book examines geometric branch-and-bound methods, such as in Lipschitzian optimization, d.c. programming and interval analysis, introduces a new concept for the rate of convergence and also analyzes several bounding operations reported in the literature.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval alsointroduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

Back Cover

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented. The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

Table of Contents

Principals and basic concepts.-The geometric branch-and-bound algorithm.-Bounding operations.- Extension for multicriteria problems.- Multicriteria discarding tests.- Extension for mixed combinatorial problems.- The circle detection problem.- Integrated scheduling and location problems.- The median line problem.- Summary and discussion.- References.- Index.

Review

From the reviews:"This little book gives a unified treatment and current state of affairs of geometric branch-and-bound methods for global optimization in low dimensions and their applications. … a valuable tool for anyone interested in the solution of low-dimensional global optimization problems. The whole text is very carefully written with special attention given to the introduction of economical notation and corresponding definitions that considerably shorten the arguments. This is particularly useful for students, but also for the working specialist." (Frank Plastria, Mathematical Reviews, September, 2013)"The book presents a collection of papers by Scholz and other authors, supplemented with some auxiliary material and discussion, and includes new details, newly edited text, and revised proofs. … an expert in global optimization and an intended user of global optimization software would benefit from owning this book on geometric B&B methods, which a recognized expert has researched." (Antanas Zilinskas, Interfaces, Vol. 43 (1), 2013)

Review Quote

From the reviews: "This little book gives a unified treatment and current state of affairs of geometric branch-and-bound methods for global optimization in low dimensions and their applications. ... a valuable tool for anyone interested in the solution of low-dimensional global optimization problems. The whole text is very carefully written with special attention given to the introduction of economical notation and corresponding definitions that considerably shorten the arguments. This is particularly useful for students, but also for the working specialist." (Frank Plastria, Mathematical Reviews, September, 2013) "The book presents a collection of papers by Scholz and other authors, supplemented with some auxiliary material and discussion, and includes new details, newly edited text, and revised proofs. ... an expert in global optimization and an intended user of global optimization software would benefit from owning this book on geometric B&B methods, which a recognized expert has researched." (Antanas Zilinskas, Interfaces, Vol. 43 (1), 2013)

Feature

Numerous examples throughout the text Easily accessible format In depth exploration of geometric branch-and-bound methods

Details ISBN1489995552 Author Daniel Scholz Short Title DETERMINISTIC GLOBAL OPTIMIZAT Language English ISBN-10 1489995552 ISBN-13 9781489995551 Media Book Format Paperback DEWEY 519.6 Series Number 63 Pages 142 Year 2014 Publication Date 2014-01-25 Imprint Springer-Verlag New York Inc. Subtitle Geometric Branch-and-bound Methods and their Applications Place of Publication New York Country of Publication United States Edition 2012th AU Release Date 2014-01-25 NZ Release Date 2014-01-25 US Release Date 2014-01-25 UK Release Date 2014-01-25 Publisher Springer-Verlag New York Inc. Edition Description 2012 ed. Series Nonconvex Optimization and Its Applications Alternative 9781461419501 Audience Undergraduate Illustrations XIV, 142 p. Country of Origin NL Product Class Description Mathematics
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