Convex Analysis and Nonlinear Optimization: Theory and Examples

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Springer Science & Business Media, 2006 - Business & Economics - 310 pages
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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

Chapter 2 Inequality Constraints
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
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About the author (2006)

Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University Adrian S. Lewis is a Professor in the School of Operations Research and Industrial Engineering at Cornell