SpringerBriefs in Optimization

Deterministic Global Optimization

An Introduction to the Diagonal Approach

Authors: Sergeyev, Yaroslav D., Kvasov, Dmitri E.

  • 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 
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eBook 44,02 €
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  • ISBN 978-1-4939-7199-2
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  • Immediate eBook download after purchase
Softcover 57,19 €
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  • ISBN 978-1-4939-7197-8
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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 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.   


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.

Reviews

“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)


Table of contents (4 chapters)

  • Lipschitz Global Optimization

    Sergeyev, Yaroslav D. (et al.)

    Pages 1-17

    Preview Buy Chapter 30,19 €
  • One-Dimensional Algorithms and Their Acceleration

    Sergeyev, Yaroslav D. (et al.)

    Pages 19-51

    Preview Buy Chapter 30,19 €
  • Diagonal Approach and Efficient Diagonal Partitions

    Sergeyev, Yaroslav D. (et al.)

    Pages 53-76

    Preview Buy Chapter 30,19 €
  • Global Optimization Algorithms Based on the Non-redundant Partitions

    Sergeyev, Yaroslav D. (et al.)

    Pages 77-120

    Preview Buy Chapter 30,19 €

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-1-4939-7199-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-1-4939-7197-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Deterministic Global Optimization
Book Subtitle
An Introduction to the Diagonal Approach
Authors
Series Title
SpringerBriefs in Optimization
Copyright
2017
Publisher
Springer-Verlag New York
Copyright Holder
The Author(s)
eBook ISBN
978-1-4939-7199-2
DOI
10.1007/978-1-4939-7199-2
Softcover ISBN
978-1-4939-7197-8
Series ISSN
2190-8354
Edition Number
1
Number of Pages
X, 136
Number of Illustrations and Tables
39 b/w illustrations
Topics