Convex Functions, Monotone Operators and Differentiability: 1364 (Lecture Notes in Mathematics, 1364) - Softcover

Phelps, Robert R.

Softcover

ISBN 10: 3540567151 ISBN 13: 9783540567158

Publisher: Springer, 1993

Synopsis

The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization. While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.

About this title

Product Description

This expanded edition contains expositions of some major results which have been obtained recently, including the proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for sub-differentials of convex functions. The material is accessible to students who have had a course in functional analysis. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and sub-differentiability of convex functions in Banach spaces, the generic continuity of monotone operators, the geometry of Banach spaces and the Radon-Nikodyn property, convex analysis, variational principles and perturbed optimization.

Edition details

• Publisher: Springer
• Publication date: 1993
• Language: English
• ISBN 10: 3540567151
• ISBN 13: 9783540567158
• Binding: Paperback
• Edition number: 2
• Number of pages: 132