ENGLISH

Convex Functions, Monotone Operators and Differentiability

By Robert R. Phelps

Book information

Publisher
Springer
Year
1993
ISBN
0387567151, 9783540567158, 9780387567150, 3540567151
LCC
QA3 .L28 no. 1364 1993,QA331.5 .L28 no. 1364
Language
english
Format
PDF
Filesize
2 MB (2198145 bytes)
Series
Lecture Notes in Mathematics 1364
Edition
2nd
Pages
127\127
DPI
300
Time added
2011-06-04 13:46:07

Description

These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.

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