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
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... interior point methods , and control - theoretic applications are typical examples . The powerful and elegant language of convex analysis unifies much of this theory . Hence our aim of writing a concise , accessible account of convex ...
... interior point revolution " in algorithms for convex optimization , fired by Nesterov and Nemirovski's seminal 1994 work [ 148 ] , and the growing interplay between convex optimization and engineering exemplified by Boyd and Vanden ...
... interior of the set DCE ( denoted int D ) if there is a real 8 > 0 satisfying x + 8B C D. In this case we say D is a neighbourhood of x . For example , the interior of R2 is R + = { x Reach x¿ > 0 } . = = We say the point x in E is the ...
... interior ( Exercises 11 , 12 , and 13 ) is devel- oped extensively in [ 167 ] ( which is also a good reference for the recession cone , Exercise 6 ) . 1. Prove the intersection of an arbitrary collection of convex sets is con- vex ...
... interior Some arguments about finite - dimensional convex sets C simplify and lose no generality if we assume C contains 0 and spans E. The following exer- cises outline this idea . 11 . 12 . ** ( Accessibility lemma ) Suppose C is a ...
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 |