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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... Order Conditions 166 172 • 8 Fixed Points 8.1 The Brouwer Fixed Point Theorem . 8.2 Selection and the Kakutani - Fan Fixed Point Theorem 8.3 Variational Inequalities . 9 Postscript : Infinite Versus Finite Dimensions 9.1 Introduction ...
... order necessary condition ) Suppose that C is a convex set in E and that the point x is a local minimizer of the function f : CR . Then for any point x in C , the directional derivative , if it exists , satisfies f ' ( x ; x - x ) ≥ 0 ...
... order necessary optimality conditions for a local minimizer of a function subject to constraints . In that case ... order condition above is sufficient for x to be a global minimizer of ƒ on C. Proposition 2.1.2 ( First order sufficient ...
... order information to tell us more about minimizers . The following elementary result from multivariate calculus is typical . Theorem 2.1.5 ( Second order conditions ) Suppose the twice contin- uously ... Conditions 17 Second Order Conditions.
... 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 minimizer . Can this happen on R ? 6. ( The ...
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 |