## 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 24

... (models such as linear and

**semidefinite**programming duality and cone polarity), we constantly emphasize the power of abstract models and notation.

5.3 Duality for Linear and

**Semidefinite**Programming . . . . . . 5.4 Convex Process Duality . . . . . . . . . . . . . . . . . . . . Nonsmooth Optimization ...

In a variety of contexts the analogous role in S” is played by the cone of positive

**semidefinite**matrices, S'. (We call a matrix X in S" positive ...

If v is a local minimizer then the Hessian V* f(a) is positive

**semidefinite**. Conversely, if the Hessian is positive definite then ä is a local minimizer.

For a matrix U in O" and a vector y in R", prove that the nearest positive

**semidefinite**matrix to U"DiagyU is U"Diagy" U. 9. " (Coercivity) Suppose that 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 |