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Minimax and Applications

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.

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  • "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."@en
  • "Classical minimax theory due to Von Neumann, together with duality and saddle point analysis, has played a critical role in optimization and game theory. Today we recognize that minimax problems and techniques appear in a broad spectrum of disciplines including game theory, optimization, and computational complexity. There are many interesting and sophisticated problems formulated as minimax applications such as, in the field of combinatorial optimization, problems of scheduling, location, allocation, packing, searching and triangulation. The contributions in this volume cover a diverse range of topics and provide a good picture of recent research and developments in minimax theory. The material in the book is accessible to graduate students as well as researchers in optimization, computer sciences and related areas."@en
  • "Classical minimax theory due to Von Neumann, together with duality and saddle point analysis, has played a critical role in optimization and game theory. Today we recognize that minimax problems and techniques appear in a broad spectrum of disciplines including game theory, optimization, and computational complexity. There are many interesting and sophisticated problems formulated as minimax applications such as, in the field of combinatorial optimization, problems of scheduling, location, allocation, packing, searching and triangulation. The contributions in this volume cover a diverse range of topics and provide a good picture of recent research and developments in minimax theory. The material in the book is accessible to graduate students as well as researchers in optimization, computer sciences and related areas."

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  • "Electronic books"@en
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  • "Minimax and Applications"
  • "Minimax and Applications"@en
  • "Minimax and applications"@en
  • "Minimax and applications"