000 05212nam a22005775i 4500
001 978-3-319-48311-5
003 DE-He213
005 20181204134420.0
007 cr nn 008mamaa
008 170301s2017 gw | s |||| 0|eng d
020 _a9783319483115
_9978-3-319-48311-5
024 7 _a10.1007/978-3-319-48311-5
_2doi
040 _aISI Library, Kolkata
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aPBKQ
_2thema
072 7 _aPBU
_2thema
082 0 4 _a515.64
_223
100 1 _aBauschke, Heinz H.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aConvex Analysis and Monotone Operator Theory in Hilbert Spaces
_h[electronic resource] /
_cby Heinz H. Bauschke, Patrick L. Combettes.
250 _a2nd ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIX, 619 p. 18 illus.
_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, Ouvrages de mathématiques de la SMC,
_x1613-5237
505 0 _aBackground -- Hilbert Spaces -- Convex Sets -- Convexity and Notation of Nonexpansiveness -- Fejer Monotonicity and Fixed Point Iterations -- Convex Cones and Generalized Interiors -- Support Functions and Polar Sets -- Convex Functions -- Lower Semicontinuous Convex Functions -- Convex Functions: Variants -- Convex Minimization Problems -- Infimal Convolution -- Conjugation -- Further Conjugation Results -- Fenchel-Rockafellar Duality -- Subdifferentiability of Convex Functions -- Differentiability of Convex Functions -- Further Differentiability Results -- Duality in Convex Optimization -- Monotone Operators -- Finer Properties of Monotone Operators -- Stronger Notions of Monotonicity -- Resolvents of Monotone Operators -- Proximity Operators -- Sums of Monotone Operators -- Zeros of Sums of Monotone Operators -- Fermat's Rule in Convex Optimization -- Proximal Minimization -- Projection Operators -- Best Approximation Algorithms.
520 _aThis reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
650 0 _aMathematical optimization.
650 0 _aAlgorithms.
650 0 _aVisualization.
650 1 4 _aCalculus of Variations and Optimal Control; Optimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26016
650 2 4 _aAlgorithms.
_0http://scigraph.springernature.com/things/product-market-codes/M14018
650 2 4 _aVisualization.
_0http://scigraph.springernature.com/things/product-market-codes/M14034
700 1 _aCombettes, Patrick L.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319483108
776 0 8 _iPrinted edition:
_z9783319483122
776 0 8 _iPrinted edition:
_z9783319839110
830 0 _aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
_x1613-5237
856 4 0 _uhttps://doi.org/10.1007/978-3-319-48311-5
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427173
_d427173