000 | 03565nam a22005415i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/0-387-31082-7 _2doi |
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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 |
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |