LEADER 05200nam 22005895 450 001 9910254287903321 005 20221128172401.0 024 7 $a10.1007/978-3-319-48311-5 035 $a(CKB)3710000001083959 035 $a(DE-He213)978-3-319-48311-5 035 $a(MiAaPQ)EBC4815423 035 $z(PPN)199767513 035 $a(PPN)199504466 035 $a(EXLCZ)993710000001083959 100 $a20170301d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvex Analysis and Monotone Operator Theory in Hilbert Spaces /$fby Heinz H. Bauschke, Patrick L. Combettes 205 $a2nd ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIX, 619 p. 18 illus.) 225 1 $aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC,$x1613-5237 311 $a3-319-48310-2 311 $a3-319-48311-0 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie ? Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016. 410 0$aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC,$x1613-5237 606 $aCalculus of variations 606 $aAlgorithms 606 $aMathematics 606 $aVisualization 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 606 $aVisualization$3https://scigraph.springernature.com/ontologies/product-market-codes/M14034 615 0$aCalculus of variations. 615 0$aAlgorithms. 615 0$aMathematics. 615 0$aVisualization. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aAlgorithms. 615 24$aVisualization. 676 $a515.64 700 $aBauschke$b Heinz H$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767388 702 $aCombettes$b Patrick L$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910254287903321 996 $aConvex Analysis and Monotone Operator Theory in Hilbert Spaces$92238302 997 $aUNINA