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Introduction to Global Optimization Exploiting Space-Filling Curves

  • Yaroslav D. Sergeyev
  • Roman G. Strongin
  • Daniela Lera

Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-x
  2. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
    Pages 1-8
  3. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
    Pages 9-46
  4. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
    Pages 47-89
  5. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
    Pages 91-116
  6. Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera
    Pages 117-118
  7. Back Matter
    Pages 119-125

About this book

Introduction

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization.  The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .  ​

Keywords

Lipschitz and Holder conditions Space-filling curves acceleration geometric algorithms global optimization information algorithms reduction of dimensionality

Authors and affiliations

  • Yaroslav D. Sergeyev
    • 1
  • Roman G. Strongin
    • 2
  • Daniela Lera
    • 3
  1. 1.Department of Computer Engineering, ModeUniversità della CalabriaRende (CS)Italy
  2. 2.Department of MathematicsN.I. Lobachevsky University of Nizhni NNizhni NovgorodRussia
  3. 3.Department of Mathematics and Computer SUniversity of CagliariCagliariItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8042-6
  • Copyright Information Yaroslav D. Sergeyev, Roman G. Strongin, Daniela Lera 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8041-9
  • Online ISBN 978-1-4614-8042-6
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • Buy this book on publisher's site
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