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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... Hence || Vƒ ( x € ) || ≤ € . Notice that the proof relies on consideration of a nondifferentiable func- tion , even though the result concerns derivatives . Exercises and Commentary The optimality conditions in this section are very ...
... Hence deduce Corollary 2.1.3 ( First order conditions for linear constraints ) . 5. Prove that the differentiable function x3 + x2 ( 1 − x1 ) 3 has a unique critical point in R2 , which is a local minimizer , but has no global ...
... hence its con- vex hull ) . This is another illustration of the idea of separation ( in this case we separate the origin and the convex hull ) . Theorems of the alternative like Gordan's theorem may be proved in a variety of ways ...
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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 |