Minimax and Applications

Ding-Zhu Du (Curatore)

Panos M. Pardalos (Curatore)

Springer-Verlag New York Inc., 2011

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.

• Curatore: Ding-Zhu Du, Panos M. Pardalos
• Editore: Springer-Verlag New York Inc.
• Collana: Nonconvex Optimization and Its Applications
• Anno: 2011
• Rilegatura: Paperback / softback
• Pagine: 296 p.
• Dimensioni: 235 x 155 mm
• EAN: 9781461335597

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