| Description |
1 online resource. |
|
text txt rdacontent |
|
computer c rdamedia |
|
online resource cr rdacarrier |
| Series |
Synthesis lectures on mathematics and statistics ; #14. 1938-1743
|
| 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 -- |
|
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 -- |
|
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 -- |
|
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 -- |
|
Solutions and hints for exercises -- Bibliography -- Authors' biographies -- Index. |
| Indexed In: |
Compendex |
|
INSPEC |
|
Google scholar |
|
Google book search |
| Subject |
Mathematical analysis.
|
|
Convex functions.
|
|
Convex geometry.
|
|
Nonsmooth optimization.
|
|
Affine set |
|
Carathéodory theorem |
|
convex function |
|
convex set |
|
directional derivative |
|
distance function |
|
Fenchel conjugate |
|
Fermat-Torricelli problem |
|
generalized differentiation |
|
Helly theorem |
|
minimal time function |
|
Nash equilibrium |
|
normal cone |
|
Radon theorem |
|
optimal value function |
|
optimization |
|
smallest enclosing ball problem |
|
set-valued mapping |
|
subdifferential |
|
subgradient |
|
subgradient algorithm |
|
support function |
|
Weiszfeld algorithm |
| Added Author |
Nguyen, Mau Nam, author.
|
|
Ebooks Corporation
|
| Related To |
Print version: 9781627052375 |
| ISBN |
9781627052382 (ebook) |
|
1627052380 (ebook) |
|
9781627052375 (paperback) |
| UPC # |
10.2200/S00554ED1V01Y201312MAS014 doi |
| OCLC # |
EBC1585295 |
|
