Convex Analysis and Nonlinear Optimization: Theory and ExamplesOptimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained. |
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Results 1-5 of 52
... nonsmooth , and from the study of functions to multifunctions . Thus , although we use certain optimization models re- peatedly to illustrate the main results ( models such as linear and semidefi- nite programming duality and cone ...
... Nonsmooth Optimization 6.1 Generalized Derivatives 6.2 Regularity and Strict Differentiability 6.3 Tangent Cones 6.4 The Limiting Subdifferential . 114 123 123 130 137 145 7 Karush - Kuhn - Tucker Theory 153 7.1 An xi Table of Contents.
... Nonsmooth Structure 213 9.1 Rademacher's Theorem 213 9.2 Proximal Normals and Chebyshev Sets 9.3 Amenable Sets and Prox - Regularity 9.4 Partly Smooth Sets . 218 228 233 10 Postscript : Infinite Versus Finite Dimensions 239 10.1 ...
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Contents
1 | |
15 | |
Chapter 3 Fenchel Duality | 33 |
Chapter 4 Convex Analysis | 65 |
Chapter 5 Special Cases | 97 |
Chapter 6 Nonsmooth Optimization | 123 |
Chapter 7 KarushKuhnTucker Theory | 153 |
Chapter 8 Fixed Points | 179 |
Chapter 9 More N onsmooth Structure | 213 |
Infinite Versus Finite Dimensions | 239 |
Chapter 11 List of Results and Notation | 253 |
Bibliography | 275 |
Index | 289 |
Other editions - View all
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |