Deterministic Global Optimization

An Introduction to the Diagonal Approach

  • Yaroslav D. Sergeyev
  • Dmitri E. Kvasov

Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-x
  2. Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 1-17
  3. Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 19-51
  4. Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 53-76
  5. Yaroslav D. Sergeyev, Dmitri E. Kvasov
    Pages 77-120
  6. Back Matter
    Pages 121-136

About this book

Introduction

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 optimization algorithms 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.   


Keywords

Deterministic global optimization Lipschitz condition derivative-free methods methods using the first Lipschitz derivatives multiextremal problems non-smooth and smooth minorants Diagonal approach efficient diagonal partitions One-dimensional algorithms Lipschitz global optimization

Authors and affiliations

  • Yaroslav D. Sergeyev
    • 1
  • Dmitri E. Kvasov
    • 2
  1. 1.Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e SistemisticaUniversità della CalabriaRende (CS)Italy
  2. 2.Department of Software and Supercomputing TechnologiesLobachevsky State UniversityNizhny NovgorodRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-7199-2
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-7197-8
  • Online ISBN 978-1-4939-7199-2
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • About this book
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