000			05059nam a22005415i 4500
001			978-1-4419-9467-7
003			DE-He213
005			20140220083729.0
007			cr nn 008mamaa
008			110418s2011 xxu| s |||| 0|eng d
020			_a9781441994677 _9978-1-4419-9467-7
024	7		_a10.1007/978-1-4419-9467-7 _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		_aBauschke, Heinz H. _eauthor.
245	1	0	_aConvex Analysis and Monotone Operator Theory in Hilbert Spaces _h[electronic resource] / _cby Heinz H. Bauschke, Patrick L. Combettes.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXVI, 468 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, Ouvrages de mathématiques de la SMC, _x1613-5237
505	0		_a Background -- 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 --  Infimal Convolution -- Conjugation -- Further Conjugation Results -- Fenchel–Rockafellar 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’s Rule in Convex Optimization -- Proximal Minimization  Projection Operators -- Best Approximation Algorithms -- Bibliographical Pointers -- Symbols and Notation -- References.
520			_aThis 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.   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.  In 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.
650		0	_aMathematics.
650		0	_aAlgorithms.
650		0	_aVisualization.
650		0	_aMathematical optimization.
650	1	4	_aMathematics.
650	2	4	_aCalculus of Variations and Optimal Control; Optimization.
650	2	4	_aAlgorithms.
650	2	4	_aVisualization.
700	1		_aCombettes, Patrick L. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441994660
830		0	_aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC, _x1613-5237
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-9467-7
912			_aZDB-2-SMA
999			_c106056 _d106056