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Global Optimization in Action

Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications

  • Book
  • © 1996

Overview

Authors:
  1. János D. Pintér

    1. Pintér Consulting Services, Dalhousie University, Canada

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Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 6)

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Global Optimization: A Brief Review

    1. Front Matter

      Pages 1-1
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    2. General Problem Statement and Special Model Forms

      • János D. Pintér
      Pages 3-19

    3. Solution Approaches

      • János D. Pintér
      Pages 21-37

  3. Partition Strategies in Global Optimization: The Continuous and the Lipschitzian Case

    1. Front Matter

      Pages 39-39
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    2. An Introduction to Partition Algorithms

      • János D. Pintér
      Pages 41-58

    3. Convergence Properties of Adaptive Partition Algorithms

      • János D. Pintér
      Pages 59-73

    4. Partition Algorithms on Intervals

      • János D. Pintér
      Pages 75-89

    5. Partition Algorithms on Multidimensional Intervals

      • János D. Pintér
      Pages 91-109

    6. Simplex Partition Strategies

      • János D. Pintér
      Pages 111-118

    7. Partition Methods on General Convex and Star Sets

      • János D. Pintér
      Pages 119-130

    8. Partition Strategies in General Lipschitz Optimization

      • János D. Pintér
      Pages 131-143

  4. Implementation Aspects, Algorithm Modifications, and Stochastic Extensions

    1. Front Matter

      Pages 145-145
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    2. Diagonally Extended Univariate Algorithms for Multidimensional Global Optimization

      • János D. Pintér
      Pages 147-154

    3. Estimation of Lipschitzian Problem Characteristics in Global Optimization

      • János D. Pintér
      Pages 155-167

    4. General Lipschitz Optimization Applying Penalty Multipliers

      • János D. Pintér
      Pages 169-172

    5. An Implementation of a Lipschitzian Global Optimization Procedure

      • János D. Pintér
      Pages 173-189

    6. Decision Making under Uncertainty: Stochastic Model Forms

      • János D. Pintér
      Pages 191-203

    7. Adaptive Stochastic Optimization Procedures

      • János D. Pintér
      Pages 205-225

    8. Estimation of Noise-Perturbed Function Values

      • János D. Pintér
      Pages 227-235
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Keywords

About this book

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s).
Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on theauthor's research, in cooperation (on applications) with a number of colleagues.
Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

Reviews

`Pinter's book can be recommended to each reader who needs a far-reaching survey of continuous and Lipschitz optimization. The book is distinguished by its vivid and informative style, the large number of areas that are touched, the lack of longwinded and overly sophisticated expositions, and the optimum balance between theory and practical applications.'
Optima, 51 (1996)

Authors and Affiliations

  • Pintér Consulting Services, Dalhousie University, Canada

    János D. Pintér

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