Stochastic Global Optimization

1. Front Matter

   Pages I-XIII

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2. Basic Concepts and Ideas

   • Anatoly Zhigljavsky, Antanas Žilinskas

   Pages 5-27

3. Global Random Search: Fundamentals and Statistical Inference

   • Anatoly Zhigljavsky, Antanas Žilinskas

   Pages 29-92

4. Global Random Search: Extensions

   • Anatoly Zhigljavsky, Antanas Žilinskas

   Pages 93-147

5. Methods Based on Statistical Models of Multimodal Functions

   • Anatoly Zhigljavsky, Antanas Žilinskas

   Pages 149-244

6. Back Matter

   Pages 245-262

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This book aims to cover major methodological and theoretical developments in the ?eld of stochastic global optimization. This ?eld includes global random search and methods based on probabilistic assumptions about the objective function. We discuss the basic ideas lying behind the main algorithmic schemes, formulate the most essential algorithms and outline the ways of their theor- ical investigation. We try to be mathematically precise and sound but at the same time we do not often delve deep into the mathematical detail, referring instead to the corresponding literature. We often do not consider the most g- eral assumptions, preferring instead simplicity of arguments. For example, we only consider continuous ?nite dimensional optimization despite the fact that some of the methods can easily be modi?ed for discrete or in?nite-dimensional optimization problems. The authors’ interests and the availability of good surveys on particular topics have in uenced the choice of material in the book. For example, there are excellent surveys on simulated annealing (both on theoretical and - plementation aspects of this method) and evolutionary algorithms (including genetic algorithms). We thus devote much less attention to these topics than they merit, concentrating instead on the issues which are not that well d- umented in literature. We also spend more time discussing the most recent ideas which have been proposed in the last few years.

• SOIA
• algorithms
• global optimization
• optimization
• population-based methods
• random search
• statistical inference about minimum
• stochastic global optimization
• stochastic models about objective function

From the reviews:

"This excellent book is written for researchers interested in global optimization. … the approach of carrying through from basic ideas to the most recent techniques will make this a valuable resource for the initiated. … Gathering together contemporary methods and developments in stochastic global optimization, this text presents four chapters." (Tom Schulte, MathDL, February, 2008)

"For global optimization, based on former monographs and articles of the authors on (global) random search, in this book global random search methods and stochastic models for the objective function are presented. … This well-written book contains many references on the field of (global) random search techniques." (Kurt Marti, Mathematical Reviews, Issue 2008 j)

"The aim of the book is to present the major methodological and theoretical developments in the field of stochastic global optimization including global random search and methods based on probabilistic assumptions about the objective function. The book contains four chapters. … The book also contains an index. The book is well written and the presentation is … self-contained." (I. M. Stancu-Minasian, Zentralblatt MATH, Vol. 1136 (14), 2008)

• School of Mathematics, Cardiff University, UK

  Anatoly Zhigljavsky

• Institute of Mathematics and Informatics, Vilnius

  Antanas Žilinskas

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