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Minimax and Applications

  • Book
  • © 1995

Overview

Editors:
  1. Ding-Zhu Du

    1. University of Minnesota, USA
      Institute of Applied Mathematics, Beijing, China

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    You can also search for this editor in PubMed   Google Scholar

  2. Panos M. Pardalos

    1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 4)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Minimax Theorems and Their Proofs

    • Stephen Simons
    Pages 1-23

  3. A Survey on Minimax Trees And Associated Algorithms

    • Claude G. Diderich, Marc Gengler
    Pages 25-54

  4. An Iterative Method for the Minimax Problem

    • Liqun Qi, Wenyu Sun
    Pages 55-67

  5. A Dual and Interior Point Approach to Solve Convex Min-Max Problems

    • Jos F. Sturm, Shuzhong Zhang
    Pages 69-78

  6. Determining the Performance Ratio of Algorithm Multifit for Scheduling

    • Feng Cao
    Pages 79-96

  7. A Study of On-Line Scheduling Two-Stage Shops

    • Bo Chen, Gerhard J. Woeginger
    Pages 97-107

  8. Maxmin Formulation of the Apportionments of Seats to a Parliament

    • Thorkell Helgason, Kurt Jörnsten, Athanasios Migdalas
    Pages 109-118

  9. On Shortest K-Edge Connected Steiner Networks with Rectilinear Distance

    • D. Frank Hsu, Xiao-Dong Hu, Yoji Kajitani
    Pages 119-127

  10. Mutually Repellant Sampling

    • Shang-Hua Teng
    Pages 129-140

  11. Geometry and Local Optimality Conditions for Bilevel Programs with Quadratic Strictly Convex Lower Levels

    • Luis N. Vicente, Paul H. Calamai
    Pages 141-151

  12. The Spherical One-Center Problem

    • Guoliang Xue, Shangzhi Sun
    Pages 153-156

  13. On Min-Max Optimization of a Collection of Classical Discrete Optimization Problems

    • Gang Yu, Panagiotis Kouvelis
    Pages 157-171

  14. Heilbronn Problem for Six Points in a Planar Convex Body

    • Andreas W. M. Dress, Lu Yang, Zhenbing Zeng
    Pages 173-190

  15. Heilbronn Problem for Seven Points in a Planar Convex Body

    • Lu Yang, Zhenbing Zeng
    Pages 191-218

  16. On the Complexity of Min-Max Optimization Problems and their Approximation

    • Ker-I Ko, Chih-Long Lin
    Pages 219-239

  17. A Competitive Algorithm for the Counterfeit Coin Problem

    • X. D. Hu, F. K. Hwang
    Pages 241-250

  18. A Minimax αβ Relaxation for Global Optimization

    • Jun Gu
    Pages 251-268

  19. Minimax Problems in Combinatorial Optimization

    • Feng Cao, Ding-Zhu Du, Biao Gao, Peng-Jun Wan, Panos M. Pardalos
    Pages 269-292

  20. Back Matter

    Pages 293-293
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Keywords

About this book

Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.

Reviews

` ... a valuable book carefully written in a clear and concise fashion. The survey papers give coherent and inspiring accounts ... coverage of algorithmic and applied topics ... is impressive. Both graduate students and researchers in fields such as optimization, computer science, production management, operations research and related areas will find this book to be an excellent source for learning about both classic and more recent developments in minimax and its applications. The editors are to be commended for their work in gathering these papers together.'
Journal of Global Optimization, 11 (1997)

Editors and Affiliations

  • University of Minnesota, USA

    Ding-Zhu Du

  • Institute of Applied Mathematics, Beijing, China

    Ding-Zhu Du

  • Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    Panos M. Pardalos

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