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Convex Analysis and Monoton...
This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. \00A0 Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "Diplom-Mathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. \00A0In 2009, he became UBCO's first "Researcher of the Year". Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005
Monografía
monografia Rebiun05913569 https://catalogo.rebiun.org/rebiun/record/Rebiun05913569 cr nn 008mamaa 110418s2011 xxu| s |||| 0|eng d 9781441994677 10.1007/978-1-4419-9467-7 doi CBUC 991000521999706712 CBUC 991049602789706706 UPVA 998557143903706 UAM 991008294232304211 CBUC 991005198186306711 CBUC 991010879378106709 CBUC 991000926199806712 CUNEF 991000449679208131 UR0331477 PBKQ bicssc PBU bicssc MAT005000 bisacsh MAT029020 bisacsh 515.64 23 Bauschke, Heinz H. Convex Analysis and Monotone Operator Theory in Hilbert Spaces Recurso electrónico-En línea] by Heinz H. Bauschke, Patrick L. Combettes New York, NY Springer New York 2011 New York, NY New York, NY Springer New York XVI, 468 p. digital XVI, 468 p. CMS Books in Mathematics, Ouvrages de mathématiques de la SMC 1613-5237 Mathematics and Statistics (Springer-11649) \00A0Background -- Hilbert Spaces -- Convex sets -- Convexity and Nonexpansiveness -- Fej´er 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 Variational Problems -- \00A0Infimal Convolution -- Conjugation -- Further Conjugation Results -- Fenchel\2013Rockafellar Duality -- Subdifferentiability -- 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 -- Sums of Monotone Operators.-Zeros of Sums of Monotone Operators -- Fermat\2019s Rule in Convex Optimization -- Proximal Minimization \00A0Projection Operators -- Best Approximation Algorithms -- Bibliographical Pointers -- Symbols and Notation -- References Accesible sólo para usuarios de la UPV Recurso a texto completo This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. \00A0 Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "Diplom-Mathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. \00A0In 2009, he became UBCO's first "Researcher of the Year". Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005 Reproducción electrónica Forma de acceso: Web Mathematics Algorithms Visualization Mathematical optimization Mathematics Calculus of Variations and Optimal Control; Optimization Algorithms Visualization Combettes, Patrick L. SpringerLink (Servicio en línea) Springer eBooks Springer eBooks Printed edition 9781441994660 CMS Books in Mathematics, Ouvrages de mathématiques de la SMC 1613-5237