{"product_id":"duality-for-nonconvex-approximation-and-optimization-hardcover","title":"Duality for Nonconvex Approximation and Optimization - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eIvan Singer\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe theory of convex optimization has been developing constantly over the past 30 years. Recently, researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called \"anticonvex\" and \"convex-anticonvex\" optimization problems. This monograph contains an exhaustive presentation of the duality theory for these classes of problems and their generalizations.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn this monograph the author presents the theory of duality for\u003c\/p\u003e \u003cp\u003enonconvex approximation in normed linear spaces and nonconvex global\u003c\/p\u003e \u003cp\u003eoptimization in locally convex spaces. Key topics include: \u003c\/p\u003e \u003cp\u003e* duality for worst approximation (i.e., the maximization of the\u003c\/p\u003e \u003cp\u003edistance of an element to a convex set)\u003c\/p\u003e \u003cp\u003e* duality for reverse convex best approximation (i.e., the minimization of\u003c\/p\u003e \u003cp\u003ethe distance of an element to the complement of a convex set)\u003c\/p\u003e \u003cp\u003e* duality for convex maximization (i.e., the maximization of a convex\u003c\/p\u003e \u003cp\u003efunction on a convex set)\u003c\/p\u003e \u003cp\u003e* duality for reverse convex minimization (i.e., the minimization of a\u003c\/p\u003e \u003cp\u003econvex function on the complement of a convex set)\u003c\/p\u003e \u003cp\u003e* duality for d.c. optimization (i.e., optimization problems involving\u003c\/p\u003e \u003cp\u003edifferences of convex functions).\u003c\/p\u003e \u003cp\u003eDetailed proofs of results are given, along with varied illustrations.\u003c\/p\u003e \u003cp\u003eWhile many of the results have been published in mathematical journals, \u003c\/p\u003e \u003cp\u003ethis is the first time these results appear in book form. In\u003c\/p\u003e \u003cp\u003eaddition, unpublished results and new proofs are provided. This\u003c\/p\u003e \u003cp\u003emonograph should be of great interest to experts in this and related\u003c\/p\u003e \u003cp\u003efields.\u003c\/p\u003e \u003cp\u003eIvan Singer is a Research Professor at the Simion Stoilow Institute of\u003c\/p\u003e \u003cp\u003eMathematics in Bucharest, and a Member of the Romanian Academy. He is\u003c\/p\u003e \u003cp\u003eone of the pioneers of approximation theory in normed linear spaces, and\u003c\/p\u003e \u003cp\u003eof generalizations of approximation theory to optimization theory. He\u003c\/p\u003e \u003cp\u003ehas been a Visiting Professor at several universities in the U.S.A., \u003c\/p\u003e \u003cp\u003eGreat Britain, Germany, Holland, Italy, and other countries, and was the\u003c\/p\u003e \u003cp\u003eprincipal speaker at an N. S. F. Regional Conference at Kent State\u003c\/p\u003e \u003cp\u003eUniversity. He is one of the editors of the journals Numerical\u003c\/p\u003e \u003cp\u003eFunctional Analysis and Optimization (since its inception in 1979), \u003c\/p\u003e \u003cp\u003eOptimization, and Revue d'analyse num\\'erique et de th\\'eorie de\u003c\/p\u003e \u003cp\u003el'approximation. His previous books include \u003cem\u003eBest Approximation in\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003eNormed Linear Spaces by Elements of Linear Subspaces\u003c\/em\u003e (Springer 1970), \u003c\/p\u003e \u003cp\u003e\u003cem\u003eThe Theory of Best Approximation and Functional Analysis\u003c\/em\u003e (SIAM 1974), \u003cem\u003eBases\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003ein Banach Spaces I, II \u003c\/em\u003e(Springer, 1970, 1981), and \u003cem\u003eAbstract Convex Analysis\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e(Wiley-Interscience, 1997).\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 356\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.84 x 9.36 x 6.22 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 16, 2006\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337265430777,"sku":"9780387283944","price":178.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/h6emiAxycY9780387283944.webp?v=1769678627","url":"https:\/\/bookscloud.io\/products\/duality-for-nonconvex-approximation-and-optimization-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}