## 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 41

Properties of

**minimizers**and maximizers of functions rely intimately on a wealth

of techniques from mathematical analysis, including tools from calculus and its

generalizations, topological notions, and more geometric ideas. The theory ...

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 A, and

the supremum (written sup A) is the least upper bound. To ensure these are ...

A (global)

**minimizer**of a function f : D → R is a point à in D at which f attains its

infimum inff = inf f(D) = inf{f(x)|r e D}. 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, ...

... 2.1 Optimality Conditions Early in multivariate calculus we learn the

significance of differentiability in finding

**minimizers**. ... consider the problem of

minimizing a function f : C → R on a set C in E. We say a point à in C is a local

**minimizer**of f ...

This book is largely devoted to the study of first order necessary optimality

conditions for a local

**minimizer**of a function ... In that case local

**minimizers**á

may not lie in the interior of the set C of interest, so the normal cone NC(#) is not

simply {0} ...

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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 |