000			04080nam a22004695i 4500
001			978-0-387-28395-1
003			DE-He213
005			20250710083941.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387283951 _a99780387283951
024	7		_a10.1007/0-387-28395-1 _2doi
082	0	4	_a515.724 _223
100	1		_aSinger, Ivan. _eauthor.
245	1	0	_aDuality for Nonconvex Approximation and Optimization _h[recurso electrónico] / _cby Ivan Singer.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXIX, 355 p. 17 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aCMS Books in Mathematics, _x1613-5237
505	0		_aPreliminaries -- Worst Approximation -- Duality for Quasi-convex Supremization -- Optimal Solutions for Quasi-convex Maximization -- Reverse Convex Best Approximation -- Unperturbational Duality for Reverse Convex Infimization -- Optimal Solutions for Reverse Convex Infimization -- Duality for D.C. Optimization Problems -- Duality for Optimization in the Framework of Abstract Convexity -- Notes and Remarks.
520			_aIn this monograph the author presents the theory of duality for nonconvex approximation in normed linear spaces and nonconvex global optimization in locally convex spaces. Key topics include: * duality for worst approximation (i.e., the maximization of the distance of an element to a convex set) * duality for reverse convex best approximation (i.e., the minimization of the distance of an element to the complement of a convex set) * duality for convex maximization (i.e., the maximization of a convex function on a convex set) * duality for reverse convex minimization (i.e., the minimization of a convex function on the complement of a convex set) * duality for d.c. optimization (i.e., optimization problems involving differences of convex functions). Detailed proofs of results are given, along with varied illustrations. While many of the results have been published in mathematical journals, this is the first time these results appear in book form. In addition, unpublished results and new proofs are provided. This monograph should be of great interest to experts in this and related fields. Ivan Singer is a Research Professor at the Simion Stoilow Institute of Mathematics in Bucharest, and a Member of the Romanian Academy. He is one of the pioneers of approximation theory in normed linear spaces, and of generalizations of approximation theory to optimization theory. He has been a Visiting Professor at several universities in the U.S.A., Great Britain, Germany, Holland, Italy, and other countries, and was the principal speaker at an N. S. F. Regional Conference at Kent State University. He is one of the editors of the journals Numerical Functional Analysis and Optimization (since its inception in 1979), Optimization, and Revue d'analyse num\'erique et de th\'eorie de l'approximation. His previous books include Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (Springer 1970), The Theory of Best Approximation and Functional Analysis (SIAM 1974), Bases in Banach Spaces I, II (Springer, 1970, 1981), and Abstract Convex Analysis (Wiley-Interscience, 1997).
650		0	_aMATHEMATICS.
650		0	_aFUNCTIONAL ANALYSIS.
650		0	_aOPERATOR THEORY.
650		0	_aMATHEMATICAL OPTIMIZATION.
650	1	4	_aMATHEMATICS.
650	2	4	_aOPERATOR THEORY.
650	2	4	_aFUNCTIONAL ANALYSIS.
650	2	4	_aOPTIMIZATION.
650	2	4	_aAPPROXIMATIONS AND EXPANSIONS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387283944
830		0	_aCMS Books in Mathematics, _x1613-5237
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-28395-1 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c56822 _d56822