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
Results 1-5 of 97
... Minimizers To find the minimizer of the convex quadratic programming test problem it suffices to find the minimizer of the n + 2 problems that compose it . Since the minimizers of the two unconstrained problems ( 10 ) are obviously y12 ...
... minimizer at 0.0 and our cubic spline approximation is quite accurate in the neighborhood of the minimizer [ -0.2 , 0.167 ] . But the approximation is not accurate in the region [ 0.167 , 1.5 ] ; it suggests that at best there is a ...
... minimizer , for the MDNLP problem , if x✶ is feasible for the problem and f ( x * ) ≤ f ( x ) for all feasible x . Definition 3. The discrete neighborhood of a point x is defined as the set of all points y , whose discrete components ...
... minimizer . However , convergence depends on how thoroughly the search can be con- ducted . Usually , an unaffordable amount of computation is required even for small problems . Another problem with this method is that the randomness ...
... Minimizer ( Theorem 17.19 ) 646 Appendix 17.E Proof of the Improved Convergence Rate of the Minimizer ( Theorem 17.21 ) 647 Appendix 17.F Equivalence between the Truncated and the Original Minimizer ( Lemma 17.27 ) 648 Appendix 17.G ...
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 |