## 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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Theory and Examples Jonathan Borwein, Adrian S. Lewis. To our families Preface Optimization is a rich and thriving mathematical discipline.

**Properties**.

**Properties**of minimizers and maximizers of functions rely intimately on a wealth of techniques from mathematical analysis, including tools from calculus and ...

Optimization studies

**properties**of minimizers and maximizers of functions. Given a set A C R, the infimum of A (written infA) is the greatest lower bound on ...

But more concretely, identifying E with R" may obscure

**properties**of a space beyond its simple Euclidean structure. As an example, in this short section we ...

... is X. The Cauchy–Schwarz inequality has an interesting refinement in S" which is crucial for variational

**properties**of eigenvalues, as we shall see.

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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 |