## 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 89

We define the norm of any

**point x**in E by ||x|| = y (x, x), and the unit ball is the set B-{seE| < 1}. Any two

**points x**and y in E satisfy the ...

A set C in E is convex if the line segment joining any two

**points x**and y in C is contained in C: algebraically, Xx + (1 — X)y € C whenever 0 < A < 1.

In this language the above result states that the point y is separated from the ... Euclidean space Y, we call a map A : E — > Y linear if any

**points x**and ...

A (global) minimizer of a function / : D — ▻ R is a

**point x**in D at which / attains its infimum inf / = inf /(D) = inf{/(x) | x € £>}.

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### 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 |