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. |
From inside the book
Results 1-5 of 55
... Constraints Optimality Conditions 2.2 Theorems of the Alternative 9 15 15 23 2.3 Max - functions . 28 3 Fenchel Duality 33 3.1 Subgradients and Convex Functions 33 3.2 The Value Function 43 3.3 The Fenchel Conjugate . 49 4 Convex ...
... σ ( A ) . ( d ) By considering matrices of the form A + al and B + ẞI , deduce Fan's inequality from von Neumann's lemma ( part ( b ) ) . Chapter 2 Inequality Constraints 2.1 Optimality Conditions Early in multivariate 14 1. Background.
Theory and Examples Jonathan Borwein, Adrian S. Lewis. Chapter 2 Inequality Constraints 2.1 Optimality Conditions Early in multivariate calculus we learn the significance of differentiability in ... Constraints 2.1 Optimality Conditions.
... constraints . In that case local minimizers ĩ may not lie in the interior of the set C of interest , so the normal cone Nc ( x ) is not simply { 0 } . The next result shows that when ƒ is convex the first order condition above is ...
... constraints on second order conditions , con- sider the framework of Corollary 2.1.3 ( First order conditions for linear constraints ) in the case E = R " , and suppose Vƒ ( x ) Є A * Y and ƒ is twice continuously differentiable near ...
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 |