000			03405nam a22004575i 4500
001			978-0-387-31082-4
003			DE-He213
005			20250710083947.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387310824 _a99780387310824
024	7		_a10.1007/0-387-31082-7 _2doi
082	0	4	_a515.64 _223
100	1		_aLucchetti, Roberto. _eauthor.
245	1	0	_aConvexity and Well-Posed Problems _h[recurso electrónico] / _cby Roberto Lucchetti.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXIV, 305 p. 46 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aCanadian Mathematical Society, _x1613-5237
505	0		_aConvex sets and convex functions: the fundamentals -- Continuity and ?(X) -- The derivatives and the subdifferential -- Minima and quasi minima -- The Fenchel conjugate -- Duality -- Linear programming and game theory -- Hypertopologies, hyperconvergences -- Continuity of some operations between functions -- Well-posed problems -- Generic well-posedness -- More exercises.
520			_aIntended for graduate students especially in mathematics, physics, and economics, this book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. The primary goal is the study of the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data. Well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of both functions and of sets. The book includes a discussion of numerous topics, including: * hypertopologies, ie, topologies on the closed subsets of a metric space; * duality in linear programming problems, via cooperative game theory; * the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions; * questions related to convergence of sets of nets; * genericity and porosity results; * algorithms for minimizing a convex function. In order to facilitate use as a textbook, the author has included a selection of examples and exercises, varying in degree of difficulty. Robert Lucchetti is Professor of Mathematics at Politecnico di Milano. He has taught this material to graduate students at his own university, as well as the Catholic University of Brescia, and the University of Pavia.
650		0	_aMATHEMATICS.
650		0	_aFUNCTIONAL ANALYSIS.
650		0	_aMATHEMATICAL OPTIMIZATION.
650		0	_aOPERATIONS RESEARCH.
650	1	4	_aMATHEMATICS.
650	2	4	_aCALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION.
650	2	4	_aOPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING.
650	2	4	_aFUNCTIONAL ANALYSIS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387287195
830		0	_aCanadian Mathematical Society, _x1613-5237
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-31082-7 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57107 _d57107