{"product_id":"minimax-and-applications-9780792336150","title":"Minimax and Applications","description":"\u003cp\u003e • Author(s): Ding-Zhu Du\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Calculus\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eTechniques 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45283617964183,"sku":"9780792336150","price":11017.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780792336150.webp?v=1769305421","url":"https:\/\/atlanticbooks.com\/products\/minimax-and-applications-9780792336150","provider":"Atlantic Books","version":"1.0","type":"link"}