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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... Corollary 2.1.3 ( First order conditions for linear constraints ) For a convex set C CE , a function f : C → R , a linear map A : E → Y ( where Y is a Euclidean space ) and a point b in Y , consider the optimization problem inf { ƒ ...
... Corollary 2.1.3 ( First order conditions for linear constraints ) in the case E = R " , and suppose Vƒ ( x ) Є A * Y and ƒ is twice continuously differentiable near . If x is a local minimizer then ya ▽ 2ƒ ( x ) y ≥ 0 for all vectors ...
... Corollary 2.1.3 ( First order conditions for linear constraints ) . 5. Prove that the differentiable function x2 + x2 ( 1 − x1 ) 3 has a unique critical point in R2 , which is a local minimizer , but has no global minimizer . Can this ...
... Corollary 2.1.3 ( First order con- ditions for linear constraints ) to prove there exists a matrix X in LOS with C – X - 1 having ( i , j ) th entry of zero for all ( i , j ) not ԼՈՏ ++ in A. ** ( BFGS update , cf. [ 80 ] ) Given a ...
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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 |