## 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

The Second Edition both corrects a few vagaries in the original and

**contains**a new chapter emphasizing the rich applicability of variational analysis to ...

(Notice we require that cones

**contain**the origin.) Examples are the positive orthant RTM = {x e Rn | each ^ > 0}, and the cone of vectors with nonincreasing ...

The smallest cone

**containing**a given set D C E is clearly R+D. The fundamental geometric idea of this book is convexity. A set C in E is convex if the line ...

Thus there is a "dual" representation of C as the intersection of all closed halfspaces

**containing**it. The set D is bounded if there is a real k satisfying ...

Deduce that the convex hull of a set D c E is well-defined as the intersection of all convex sets

**containing**D. 2. (a) Prove that if the set C C E is convex ...

### What people are saying - Write a review

### Contents

Chapter 2 Inequality Constraints | 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 |

### Other editions - View all

Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |