Convex Analysis

by R. Tyrrell Rockafellar

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.


This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.
--back cover

Genres: Mathematics, Textbooks

470 pages, Paperback

First published January 1, 1970

Reviews

[Matus · Rating 5 out of 5]

I HAVE LOCATED THE MASTER

[Zhitao Fan · Rating 5 out of 5]

This book is the classic of convex analysis and optimization theory. The intimate relationship of convex function and convex set clear many of my doubts. The book introduces conjugate function and dualities, which balances the geometric intuition and mathematical rigorous. Hence the book gives a natural introduction of subgradients. The last two chapters are aiming at the theoretical analysis of the optimization problems. This book serves greatly to those who are interested in the optimization theory since there fair amount of introduction.

[dead letter office · Rating 3 out of 5]

rough read, good reference.