Overview
- Editors:
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Ding-Zhu Du
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University of Minnesota, USA
Institute of Applied Mathematics, Beijing, China
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Panos M. Pardalos
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Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA
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Table of contents (18 chapters)
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- Claude G. Diderich, Marc Gengler
Pages 25-54
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- Jos F. Sturm, Shuzhong Zhang
Pages 69-78
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- Bo Chen, Gerhard J. Woeginger
Pages 97-107
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- Thorkell Helgason, Kurt Jörnsten, Athanasios Migdalas
Pages 109-118
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- D. Frank Hsu, Xiao-Dong Hu, Yoji Kajitani
Pages 119-127
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- Luis N. Vicente, Paul H. Calamai
Pages 141-151
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- Guoliang Xue, Shangzhi Sun
Pages 153-156
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- Gang Yu, Panagiotis Kouvelis
Pages 157-171
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- Andreas W. M. Dress, Lu Yang, Zhenbing Zeng
Pages 173-190
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- Feng Cao, Ding-Zhu Du, Biao Gao, Peng-Jun Wan, Panos M. Pardalos
Pages 269-292
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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.
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
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University of Minnesota, USA
Ding-Zhu Du
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Institute of Applied Mathematics, Beijing, China
Ding-Zhu Du
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Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA
Panos M. Pardalos