Convex Analysis and Nonlinear Optimization

Optimization 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.

Contents

Preface

1. Background.
2. Inequality constraints.
3. Fenchel duality.
4. Convex analysis.
5. Special cases.
6. Nonsmooth optimization.
7. The Karush-Kuhn-Tucker Theorem.
8. Fixed points.
9. Postscript : infinite versus finite dimensions.
10. List of results and notation.

Bibliography
Index