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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Theory and Examples Jonathan M. Borwein, Adrian S. Lewis. Jonathan M. Borwein Adrian S. Lewis Convex Analysis and Nonlinear Optimization Theory and Examples Second Edition Canadian Mathematical Society Société mathématique du Canada ...
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Theory and Examples Jonathan M. Borwein, Adrian S. Lewis. Contents Preface 1 Background vii 1 1.1 Euclidean Spaces 1 2.1 1.2 Symmetric Matrices 2 Inequality Constraints Optimality Conditions 2.2 Theorems of the Alternative 9 15 15 23 2.3 ...
Theory and Examples Jonathan M. Borwein, Adrian S. Lewis. 7 Karush - Kuhn - Tucker Theory 153 7.1 An Introduction to Metric Regularity 153 7.2 The Karush Kuhn - Tucker Theorem 160 7.3 Metric Regularity and the Limiting Subdifferential ...
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Contents
Chapter 1 Background | 1 |
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 |