## 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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In this case we refer to £ as an

**optimal solution**of the optimization problem info f. For a positive real 6 and a function g :(0, 6) – R, we define liminf q(t) = lim inf t|0 g(t) t| 0 (0,t) 9 and lim supg(t) = lim supg. t|0 t10 (0,i) ...

(b) Prove the problem has an

**optimal solution**using Section 1.2, Exercise 14. (c) Use Corollary 2.1.3 (First order conditions for linear constraints) to find the solution. (The solution is called the BFGS update of C" under the secant ...

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### Contents

15 | |

Fenchel Duality | 33 |

Convex Analysis | 65 |

Special Cases | 97 |

Nonsmooth Optimization | 123 |

KarushKuhnTucker Theory | 153 |

Fixed Points | 179 |

Infinite Versus Finite Dimensions | 209 |

List of Results and Notation | 221 |

Bibliography | 241 |

Index | 253 |

### Other editions - View all

Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |