## 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 54

The theory underlying current computational optimization techniques grows ever more sophisticated-duality-based algorithms,

**interior**point methods, ...

The “

**interior**point revolution” in algorithms for convex optimization, fired by Nesterov and Nemirovski's seminal 1994 work [148], and the growing interplay ...

For example, the

**interior**of R' is R'l = {a e R” each a' = 0}. We say the point x in E is the limit of the sequence of points a ', a.

The theory of the relative

**interior**(Exercises 11, 12, and 13) is developed extensively in [167] (which is also a good reference for the recession cone, ...

The relative

**interior**Some arguments about finite-dimensional convex sets C simplify and lose no generality if we assume C contains 0 and spans E. The ...

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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 |