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 33
... Exercise 10 . Exercises and Commentary Good general references are [ 177 ] for elementary real analysis and [ 1 ] for lin- ear algebra . Separation theorems for convex sets originate with Minkowski [ 142 ] . The theory of the relative ...
... ) Doubly stochastic matrices are convex com- binations of permutation matrices . We defer the proof to a later section ( Section 4.1 , Exercise 22 ) . Exercises and Commentary Fan's inequality ( 1.2.2 ) appeared in 10 1. Background.
Theory and Examples Jonathan Borwein, Adrian S. Lewis. Exercises and Commentary Fan's inequality ( 1.2.2 ) appeared in [ 73 ] , but is closely related to earlier work of von Neumann [ 184 ] . The condition for equality is due to [ 180 ] ...
... Exercises and Commentary The optimality conditions in this section are very standard ( see for example [ 132 ] ) . The simple variational principle ( Proposition 2.1.7 ) was suggested by [ 95 ] . 1. Prove the normal cone is a closed ...
... ( Exercise 6 ) : any point c not lying in the finitely generated cone C = m R ... Commentary Gordan's theorem appeared in [ 84 ] , and the Farkas lemma appeared in [ 75 ] . The standard modern approach to theorems of the alternative ( Exercises ...
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 |