Convex Functions, Monotone Operators and Differentiability

Robert R. Phelps

ISBN 10: 3540567151 / ISBN 13: 9783540567158

Published by Springer, Berlin, Springer, 1993

About this Item

Neuware - In the three and a half years since the first edition to these notes was written there has been progress on a number of relevant topics. D. Preiss answered in the affirmative the decades old question of whether a Banach space with an equivalent Gateaux differentiable norm is a weak Asplund space, while R. Haydon constructed some very ingenious examples which show, among other things, that the converse to Preiss' theorem is false. S. Simons produced a startlingly simple proof of Rockafellar's maximal monotonicity theorem for subdifferentials of convex functions. G. Godefroy, R. Deville and V. Zizler proved an exciting new version ofthe Borwein-Preiss smooth variational prin ciple. Other new contributions to the area have come from J. Borwein, S. Fitzpatrick, P. Kenderov, 1. Namioka, N. Ribarska, A. and M. E. Verona and the author. Some ofthe new material and substantial portions ofthe first edition were used in a one-quarter graduate course at the University of Washington in 1991 (leading to a number of corrections and improvements) and some of the new theorems were presented in the Rainwater Seminar. An obvious improvement is due to the fact that I learned to use '!EX. The task of converting the original MacWrite text to '!EXwas performed by Ms. Mary Sheetz, to whom I am extremely grateful.

Seller Inventory # 9783540567158

Bibliographic Details

• Title: Convex Functions, Monotone Operators and Differentiability
• Publisher: Springer, Berlin, Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 3540567151
• ISBN 13: 9783540567158
• Binding: Taschenbuch
• Edition: 2nd Edition
• Condition: Neu
• Dimensions: 236W x 157H x 9D millimeters 236 millimeters width by 157 millimeters height by 9 millimeters depth
• Weight: 214 grams

About this title

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.

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.