Minimax and Applications

丛 书 名：Nonconvex Optimization and Its Applications

版本说明：1

作     者：Ding-Zhu Du Panos M. Pardalos 

I S B N：(纸本) 9780792336150;9781461335597 

出 版 社：Springer New York  NY 

出 版 年：1000年

页      数：XIV, 296页

主 题 词：Algorithms Discrete Mathematics in Computer Science Computational Mathematics and Numerical Analysis 

摘      要：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.