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Convex analysis and monotone operato...

Bauschke, Heinz H.

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Convex analysis and monotone operator theory in Hilbert spaces

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convex analysis and monotone operator theory in Hilbert spaces/ by Heinz H. Bauschke, Patrick L. Combettes.
作者:	Bauschke, Heinz H.
其他作者:	Combettes, Patrick L.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xix, 619 p. :ill., digital ;24 cm.
內容註:	Background -- 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.
Contained By:	Springer eBooks
標題:	Hilbert space. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-48311-5
ISBN:	9783319483115

Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H.

Convex analysis and monotone operator theory in Hilbert spaces[electronic resource] /by Heinz H. Bauschke, Patrick L. Combettes. - 2nd ed. - Cham :Springer International Publishing :2017. - xix, 619 p. :ill., digital ;24 cm. - CMS books in mathematic,1613-5237. - CMS books in mathematics..

Background -- 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.

ISBN: 9783319483115

Standard No.: 10.1007/978-3-319-48311-5doiSubjects--Topical Terms:

558371
Hilbert space.

LC Class. No.: QA322.4 / .B38 2017

Dewey Class. No.: 515.733

Convex analysis and monotone operator theory in Hilbert spaces
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300 $a xix, 619 p. : $b ill., digital ; $c 24 cm.
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505 0 $a Background -- 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.
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650 0 $a Approximation theory. $3 628068
650 0 $a Monotone operators. $3 705273
650 0 $a Nonlinear functional analysis. $3 576798
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650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Algorithms. $3 536374
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