Convex Analysis and Nonlinear Optimization: Theory and Examples

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Springer Science & Business Media, Jun 29, 2013 - Mathematics - 273 pages

Optimization 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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Contents

Inequality Constraints
15
Fenchel Duality
33
Convex Analysis
65
Special Cases
97
Nonsmooth Optimization
123
KarushKuhnTucker Theory
153
Fixed Points
179
Infinite Versus Finite Dimensions
209
List of Results and Notation
221
Bibliography
241
Index
253
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