Introduction to Global Optimization Exploiting Space-Filling Curves

1. Front Matter

   Pages i-x

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2. Introduction

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

   Pages 1-8

3. Approximations to Peano Curves: Algorithms and Software

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

   Pages 9-46

4. Global Optimization Algorithms Using Curves to Reduce Dimensionality of the Problem

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

   Pages 47-89

5. Ideas for Acceleration

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

   Pages 91-116

6. A Brief Conclusion

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

   Pages 117-118

7. Back Matter

   Pages 119-125

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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 .  ​

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

“This book is an excellent introduction to global optimization methods based on space-filling curves. The very useful content and engaging style of presentation make it a pleasant, interesting, and valuable read, and I enthusiastically recommend it to anyone interested in optimization.” (Sergiy Butenko, SIAM Review, Vol. 57 (1), March, 2015)

“The book gives an introduction to the subject and describes a number of non-trivial algorithms combining sophisticated ideas of pure mathematics with numerical methods. … this is an excellent book written by the world-leading authorities in the field of global optimization. The book nicely describes powerful ideas and algorithms, which could certainly be very useful to anybody working in numerical global optimization.” (Anatoly Zhigljavsky, Journal of Global Optimization, Vol. 60, 2014)

• Department of Computer Engineering, Mode, Università della Calabria, Rende (CS), Italy

  Yaroslav D. Sergeyev

• Department of Mathematics, N.I. Lobachevsky University of Nizhni N, Nizhni Novgorod, Russia

  Roman G. Strongin

• Department of Mathematics and Computer S, University of Cagliari, Cagliari, Italy

  Daniela Lera

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