## 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. |

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Results 1-5 of 32

Given any set D C E, the linear span of D, denoted span (D), is the smallest linear

**subspace**containing D. It consists exactly of all linear combinations of ...

Given a

**subspace**G of E, the orthogonal complement of G is the

**subspace**G+ = {ye E|(t, y) = 0 for all a e G}, so called because we can write E as a direct ...

(e) If Y is a Euclidean space, the map A : E → Y is linear, and N(A) O 0" (C) is a linear

**subspace**, prove AC is closed. Show this result can fail without ...

(b) Prove that a set is affine if and only if it is a translate of a linear

**subspace**. (c) Prove affD is the set of all affine combinations of elements of D.

(e) For any point a in D, prove affD = a +span (D–a), and deduce the linear

**subspace**span (D - a) is independent of a. 13. “ (The relative interior) (We use ...

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### 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 |