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


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.


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
  • 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