000 03565nam a22005415i 4500
001 978-0-387-31082-4
003 DE-He213
005 20161121231025.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387310824
_9978-0-387-31082-4
024 7 _a10.1007/0-387-31082-7
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aPBU
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aMAT029020
_2bisacsh
082 0 4 _a515.64
_223
100 1 _aLucchetti, Roberto.
_eauthor.
245 1 0 _aConvexity and Well-Posed Problems
_h[electronic resource] /
_cby Roberto Lucchetti.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2006.
300 _aXIV, 305 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCMS Books in Mathematics,
_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 _aCalculus of variations.
650 0 _aOperations research.
650 0 _aManagement science.
650 1 4 _aMathematics.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aOperations Research, Management Science.
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387287195
830 0 _aCMS Books in Mathematics,
_x1613-5237
856 4 0 _uhttp://dx.doi.org/10.1007/0-387-31082-7
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507440
_d507440