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© 2016

Evolutionary Global Optimization, Manifolds and Applications

  • Presents powerful techniques for solving global optimization problems

  • Shows simple ways to deal with optimization problems involving proper nonlinear manifolds

  • Discusses in detail applications to real-world problems

  • Offers an overview of current metaheuristics paradigms

Book

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 43)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introductory Information

    1. Front Matter
      Pages 1-1
    2. Hime Aguiar e Oliveira Junior
      Pages 3-12
    3. Hime Aguiar e Oliveira Junior
      Pages 13-23
  3. Global Optimization on Manifolds

    1. Front Matter
      Pages 25-25
    2. Hime Aguiar e Oliveira Junior
      Pages 27-46
    3. Hime Aguiar e Oliveira Junior
      Pages 47-73
  4. Further Applications of Fuzzy ASA

    1. Front Matter
      Pages 75-75
    2. Hime Aguiar e Oliveira Junior
      Pages 77-92
    3. Hime Aguiar e Oliveira Junior
      Pages 93-107
    4. Hime Aguiar e Oliveira Junior
      Pages 109-132
    5. Hime Aguiar e Oliveira Junior
      Pages 133-134
  5. Back Matter
    Pages 135-137

About this book

Introduction

This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages.

Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory. Many necessary definitions and fundamental results are provided, with the formal mathematical requirements limited to a minimum, while the focus is kept firmly on continuous problems. The book offers a valuable resource for students, researchers and practitioners. It is suitable for university courses on optimization and for self-study.

 

Keywords

Topological Manifolds Smooth Manifolds Fuzzy Optimization Fuzzy ASA Adaptive Simulated Annealing Nash Equilibrium Problems Constrained Optimization Game Theory Applications Finite Strategic Games

Authors and affiliations

  1. 1.National Cinema AgencyRio de JaneiroBrazil

Bibliographic information

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