Stochastic Global Optimization

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.

List of contents

Basic Concepts and Ideas.- Global Random Search: Fundamentals and Statistical Inference.- Global Random Search: Extensions.- Methods Based on Statistical Models of Multimodal Functions.

About the author

Jack Noonan is a postdoctoral researcher at Cardiff University School of Mathematics, UK. At Cardiff University, he received a PhD on applied probability and statistics in 2021 and received a BSc in Mathematics, Operational Research and Statistics in 2017. His areas of research include high-dimensional optimization and inference, change-point detection, group testing, modelling of epidemics and missing data.

Anatoly Zhigljavsky is a professor of mathematics and statistics at Cardiff University, UK. He holds this post since 1997. He received PhD (and then habilitation) on applied probability and computational mathematics in 1981 (respectively, in 1986) at St. Petersburg State University. He is the author or co-author of 12 monographs on the topics of stochastic global optimization (five), time series analysis (four), optimal experimental design (two) and dynamical systems (one); editor/co-editor of 12 books or special issues of journals on the topics above, the author of more than 200 research papers in refereed journals, organizer of several major conferences on kernel methods in machine learning, time series analysis, experimental design, and global optimization. Professor Zhigljavsky is a recipient of a prestigious Constantine Caratheodory award (2019) by the International Society for Global Optimization for his life-time achievement in the field of stochastic global optimization.

Summary

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.

Additional text

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)

Report

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)

Product details

• Authors: Anatol Zhigljavsky, Anatoly Zhigljavsky, Antanas Zilinskas, Antanasz Zilinskas
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 21.10.2010
• EAN: 9781441944856
• ISBN: 978-1-4419-4485-6
• No. of pages: 262
• Dimensions: 159 mm x 15 mm x 238 mm
• Weight: 416 g
• Illustrations: X, 262 p.
• Series: Springer Optimization and Its Applications; Springer Optimization and Its Applications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Stochastik, C, Optimization, Statistics, Wahrscheinlichkeitsrechnung und Statistik, Mathematics and Statistics, Statistical Theory and Methods, Probability Theory and Stochastic Processes, Probability & statistics, Probabilities, Stochastics, Probability Theory, Mathematical optimization