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Deterministic Global Optimization

An Introduction to the Diagonal Approach

  • Book
  • © 2017

Overview

Authors:
  1. Yaroslav D. Sergeyev

    1. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Università della Calabria, Rende (CS), Italy

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  2. Dmitri E. Kvasov

    1. Department of Software and Supercomputing Technologies, Lobachevsky State University, Nizhny Novgorod, Russia

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  • Contains a survey on Lipschitz deterministic global optimization methods
  • Outlines a new class of algorithms
  • Maximizes reader insights into multiextremal continuous problems
  • Includes case studies
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-x
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  2. Lipschitz Global Optimization

    • Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 1-17

  3. One-Dimensional Algorithms and Their Acceleration

    • Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 19-51

  4. Diagonal Approach and Efficient Diagonal Partitions

    • Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 53-76

  5. Global Optimization Algorithms Based on the Non-redundant Partitions

    • Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 77-120

  6. Back Matter

    Pages 121-136
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Keywords

About this book

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 optimizationalgorithms 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.   


Reviews

“The topic of the book and the class of algorithms described in the volume are of an indisputable interest … . the book under review gives an important contribution to the existing optimization literature. It will be interesting to a broad scientific community working with application and development of global optimization algorithms. Engineers, researchers, and students will find this volume extremely useful and inspiring.” (Timoleon Kipouros, Journal of Global Optimization, Vol. 80, 2021)




“The book is well-organized, self-contained, and technically sound. I think it will be highly requested not only by researchers in the field of global (and local) optimization but also by engineers, graduate and postgraduate students, and practitioners.” (Antanas Zilinskas, Optimization Letters, Vol. 15, 2021)

“The authors of this brief book consider global optimization problems, in which the Lipschitz continuity condition is satisfied. … This book will be for sure interesting for the researchers and PhD students working in the area of global optimization.” (Marcin Anholcer, zbMATH 1371.90112, 2017)


Authors and Affiliations

  • Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Università della Calabria, Rende (CS), Italy

    Yaroslav D. Sergeyev

  • Department of Software and Supercomputing Technologies, Lobachevsky State University, Nizhny Novgorod, Russia

    Dmitri E. Kvasov

About the authors

Yaroslav D. Sergeyev is the President of the International Society of Global Optimization and Distinguished Professor at the University of Calabria, Italy. He is also a Member of the University International Council and Professor at Lobachevsky Nizhniy Novgorod State University, Russia.  His research interests include numerical analysis, global optimization, infinity computing and calculus, philosophy of computations, set theory, number theory, fractals, parallel computing, and interval analysis. 

Dmitri Kvasov is an Assistant Professor at DIMES, University of Calabria, Rende,Italy and Senior Programmer at the Institute of Information Technology, Mathematics and Mechanics at Lobachevsky State University of Nizhny Novgorod, Russia. His research interest includes numerical analysis, continuous global optimization, and infinity computing.

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