## 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 82

The set D is bounded if there is a

**real**k satisfying kB D D, ... Given a set D in E, we call a

**function**f : D → R. continuous (on D) if f(x') — f(x) for ...

For a positive

**real**6 and a

**function**g : (0, 6) – R, we define lim inf q(t) = lim inf I t|0 g(t) # '', g and lim supg(t) = lim supg. t|0 t10 (0,i) The limit ...

Proposition 1.1.5 For a convex set C C E, a convex

**function**f : C → R. has bounded ... are [177 for elementary

**real**analysis and [1] for linear algebra.

10 * (Convex growth conditions) (a) Find a

**function**with bounded level sets which ... C is a convex set in E. (a) Prove clo' C. C + eB for any

**real**e > 0.

... Euclidean space which “feels” very different from R”: the space S" of n X m

**real**symmetric matrices. ... In this way we define a

**function**A : S" – R.".

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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 |