## 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

... be approached through our main variational tools: subgradients and optimality

**conditions**, the many guises of duality, metric regularity and so forth.

... Regularity 153 7.2 The Karush-Kuhn-Tucker Theorem 160 7.3 Metric Regularity and the Limiting Subdifferential 166 7.4 Second Order

**Conditions**172 8 Fixed ...

Another example is the stronger

**condition**liminf ^p>0, (1.1.4) where we define liminf ... for convex functions these two growth

**conditions**are equivalent.

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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 |