## 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 29

These exercises fall into three categories, marked with

**zero**, one, or two asterisks, respectively, as follows: examples that illustrate the ideas in the text or easy expansions of sketched proofs; important pieces of additional theory ...

... matrices with all nonnegative entries, and each row and column summing to one) and the set P” of permutation matrices (square matrices with all entries

**Zero**or one, and with exactly one entry of one in each row and in each column).

For a matrix A in M” we define the singular values of A by g(A) = V/X(ATA) for i = 1,2,...,n, and hence define a map a : M” – R”. (Notice

**zero**may be a singular value.) X 0 A" | | | a(A) A 0 | 1.2 Symmetric Matrices 13.

(Matrix completion [77]) For a set A c{(i,j)|1 < i < j < n}, suppose the subspace L CS” of matrices with (i,j)th entry of

**zero**for all (i,j) in A satisfies Ln S't # 0. By considering the problem (for C eS'') inf{(C, X) – log det X |X e ...

You have reached your viewing limit for this book.

### What people are saying - Write a review

### 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 |