Description |
1 online resource. |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
Series |
Synthesis lectures on mathematics and statistics ; #14. 1938-1743
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Reproduction |
Electronic reproduction. Perth, W.A. Available via World Wide Web. |
Note |
Description based on online resource; title from PDF title page (Morgan & Claypool, viewed on January 13, 2014). |
Bibliography |
Includes bibliographical references (pages 195-197) and index. |
Contents |
1. Convex sets and functions -- 1.1 Preliminaries -- 1.2 Convex sets -- 1.3 Convex functions -- 1.4 Relative interiors of convex sets -- 1.5 The distance function -- 1.6 Exercises for chapter 1 -- |
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2. Subdifferential calculus -- 2.1 Convex separation -- 2.2 Normals to convex sets -- 2.3 Lipschitz continuity of convex functions -- 2.4 Subgradients of convex functions -- 2.5 Basic calculus rules -- 2.6 Subgradients of optimal value functions -- 2.7 Subgradients of support functions -- 2.8 Fenchel conjugates -- 2.9 Directional derivatives -- 2.10 Subgradients of supremum functions -- 2.11 Exercises for chapter 2 -- |
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3. Remarkable consequences of convexity -- 3.1 Characterizations of differentiability -- 3.2 Carathéodory theorem and Farkas Lemma -- 3.3 Radon theorem and Helly theorem -- 3.4 Tangents to convex sets -- 3.5 Mean value theorems -- 3.6 Horizon cones -- 3.7 Minimal time functions and Minkowski gauge -- 3.8 Subgradients of minimal time functions -- 3.9 Nash equilibrium -- 3.10 Exercises for chapter 3 -- |
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4. Applications to optimization and location problems -- 4.1 Lower semicontinuity and existence of minimizers -- 4.2 Optimality conditions -- 4.3 Subgradient methods in convex optimization -- 4.4 The Fermat-Torricelli problem -- 4.5 A generalized Fermat-Torricelli problem -- 4.6 A generalized Sylvester problem -- 4.7 Exercises for chapter 4 -- |
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Solutions and hints for exercises -- Bibliography -- Authors' biographies -- Index. |
Indexed In: |
Compendex |
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INSPEC |
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Google scholar |
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Google book search |
Subject |
Mathematical analysis.
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Convex functions.
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Convex geometry.
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Nonsmooth optimization.
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Affine set |
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Carathéodory theorem |
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convex function |
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convex set |
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directional derivative |
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distance function |
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Fenchel conjugate |
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Fermat-Torricelli problem |
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generalized differentiation |
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Helly theorem |
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minimal time function |
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Nash equilibrium |
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normal cone |
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Radon theorem |
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optimal value function |
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optimization |
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smallest enclosing ball problem |
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set-valued mapping |
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subdifferential |
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subgradient |
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subgradient algorithm |
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support function |
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Weiszfeld algorithm |
Added Author |
Nguyen, Mau Nam, author.
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Ebooks Corporation
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Related To |
Print version: 9781627052375 |
ISBN |
9781627052382 (ebook) |
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1627052380 (ebook) |
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9781627052375 (paperback) |
UPC # |
10.2200/S00554ED1V01Y201312MAS014 doi |
OCLC # |
EBC1585295 |
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