Global Optimization with Non-Convex Constraints

1. Front Matter

   Pages i-xxviii

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2. Global Optimization Algorithms as Decision Procedures. Theoretical Background and Core Univariate Case

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 3-51

   3. Global Optimization Algorithms as Statistical Decision Procedures — The Information Approach

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 53-125

   4. Core Global Search Algorithm and Convergence Study

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 127-229

   5. Global Optimization Methods as Bounding Procedures — The Geometric Approach

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 231-315

3. Generalizations for Parallel Computing, Constrained and Multiple Criteria Problems

   1. Front Matter

      Pages 317-317

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   2. Parallel Global Optimization Algorithms and Evaluation of the Efficiency of Parallelism

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 319-377

   3. Global Optimization under Non-Convex Constraints — The Index Approach

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 379-418

   4. Algorithms for Multiple Criteria Multiextremal Problems

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 419-441

4. Global Optimization in Many Dimensions. Generalizations through Peano Curves

   1. Front Matter

      Pages 443-443

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   2. Peano-Type Space-Filling Curves as Means for Multivariate Problems

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 445-549

   3. Multidimensional Parallel Algorithms

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 551-610

   4. Multiple Peano Scannings and Multidimensional Problems

      • Roman G. Strongin, Yaroslav D. Sergeyev

      Pages 611-649

5. Back Matter

   Pages 651-703

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Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro­ bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op­ tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu­ ral consequence of the raising complexity of these objects, greatly com­ plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer­ aided simulation of an object's behavior, based on numerical experiments with its mathematical model.

• Computer
• STATISTICA
• algorithms
• computer science
• global optimization
• mathematics
• optimization
• science

• Nizhni Novgorod State University, Nizhni Novgorod, Russia

  Roman G. Strongin, Yaroslav D. Sergeyev

• Institute of Systems Analysis and Information Technology, University of Calabria, Rende, Italy

  Yaroslav D. Sergeyev

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