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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... subset A of R we define - АС AC = { λα | λ ε Λ , τε C } . = Given another Euclidean space Y , we can consider the Cartesian product Euclidean space Ex Y , with inner product defined by ( ( e , x ) , ( f , y ) ) ( e , f ) + ( x , y ) ...
... subset G of D is open in D if there is an open set UCE with G = DNU . Much of the beauty of convexity comes from duality ideas , interweaving geometry and topology . The following result , which we prove a little later , is both typical ...
... subset of E. ( i ) If y is any point in E , prove there is a unique nearest point ( or best approximation ) Pc ( y ) to y in C , characterized by ( y - Pc ( y ) , x - Pc ( y ) ) < 0 for all x € C. ( ii ) For any point ≈ in C , deduce ...
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Contents
7 | |
15 | |
Fenchel Duality | 33 |
Convex Analysis | 65 |
Special Cases | 97 |
Nonsmooth Optimization | 123 |
Fixed Points | 183 |
Infinite Versus Finite Dimensions | 209 |
List of Results and Notation | 221 |
Bibliography | 241 |
Other editions - View all
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |