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 68
... Finite Partially Ordered Sets 3 BORWEIN / LEWIS Convex Analysis and Nonlinear Optimization , Second Edition 4 LEVIN / LUBINSKY Orthogonal Polynomials for Exponential Weights 5 KANE Reflection Groups and Invariant Theory 6 PHILLIPS Two ...
... finite - dimensional convex analysis already ex- ist . Rockafellar's classic Convex Analysis [ 167 ] has been indispensable and ubiquitous since the 1970s , and a more general sequel with Wets , Varia- tional Analysis [ 168 ] , appeared ...
... Finite Dimensional Vector Spaces [ 90 ] , ease of ex- tension beyond finite dimensions substantially motivates our choice of ap- proach . Where possible , we have chosen a proof technique permitting those readers familiar with ...
... Finite Dimensions 239 10.1 Introduction . . 239 10.2 Finite Dimensionality 241 10.3 Counterexamples and Exercises 10.4 Notes on Previous Chapters 244 • 248 11 List of Results and Notation 11.1 Named Results 11.2 Notation . Bibliography ...
... finite - dimensional vector space over the reals R , equipped with an inner product ( , ) . We would lose no generality if we considered only the space Rn of real ( column ) n - vectors ( with its standard inner product ) , but a more ...
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 |