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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... Gâteaux de Provence Gâteau aux Pistaches Gâteaux de Compiègne Brioches de Paris du Palais Royal Gâteau à la Crême Gâteau à l'Huile Gâteaux de Brie Gâteaux Allemands Gâteaux de Florence . Gâteaux du Puits d'Amour --- 41 42 43 44 RELI ...
... Gâteaux functional ( 2 ) . It can also be considered over the set of vector functions x = ( x ( t ) , ... , x ( t ) ) We denote ( 2 ) with X being a vector from As by = M S 9m 9m ( x ( t ) , t ) dt " . • ( 4 ) Clearly , not only the sum ...
... Gâteaux differentiable at x Є X , if there exists LЄ L ( X , Y ) such that lim X ÷ 0 f ( x + Xh ) f ( x )入= Lh for all hЄ X. The operator L € L ( X , Y ) is called the Gâteaux derivative of ƒ at x Є X and is denoted by f ' ( x ) . We ...
... Gâteaux- differentiability " . This provides a method for the " construction " of the subdif- ferential for a given functional . A functional f : X → IR , where X is a H - space is said to be one - sided directional Gâteaux ...
... Gâteaux - differential of ƒ at ro with respect to the direction h . If ƒ ′ ( xo , h ) = −ƒ ' ( xo , -h ) Vh Є X , then ƒ is Gâteaux - differentiable at xo . It can be readily shown that f ' ( xo , ) is a convex , positively homogeneous ...
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 |