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Minimax and Applications

  • Ding-Zhu Du
  • Panos M. Pardalos

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Stephen Simons
    Pages 1-23
  3. Claude G. Diderich, Marc Gengler
    Pages 25-54
  4. Liqun Qi, Wenyu Sun
    Pages 55-67
  5. Bo Chen, Gerhard J. Woeginger
    Pages 97-107
  6. Thorkell Helgason, Kurt Jörnsten, Athanasios Migdalas
    Pages 109-118
  7. D. Frank Hsu, Xiao-Dong Hu, Yoji Kajitani
    Pages 119-127
  8. Shang-Hua Teng
    Pages 129-140
  9. Guoliang Xue, Shangzhi Sun
    Pages 153-156
  10. Andreas W. M. Dress, Lu Yang, Zhenbing Zeng
    Pages 173-190
  11. Lu Yang, Zhenbing Zeng
    Pages 191-218
  12. X. D. Hu, F. K. Hwang
    Pages 241-250
  13. Feng Cao, Ding-Zhu Du, Biao Gao, Peng-Jun Wan, Panos M. Pardalos
    Pages 269-292
  14. Back Matter
    Pages 293-293

About this book

Introduction

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.

Keywords

algorithms Approximation combinatorial optimization complexity computation game theory geometry networks optimization programming scheduling

Editors and affiliations

  • Ding-Zhu Du
    • 1
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.University of MinnesotaUSA
  2. 2.Institute of Applied MathematicsBeijingChina
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-3557-3
  • Copyright Information Springer-Verlag US 1995
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-3559-7
  • Online ISBN 978-1-4613-3557-3
  • Series Print ISSN 1571-568X
  • Buy this book on publisher's site