Lecture Notes in Mathematics

Convex Functions, Monotone Operators and Differentiability

Authors: Phelps, Robert R.

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About this book

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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-3-662-21569-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Convex Functions, Monotone Operators and Differentiability
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1364
Copyright
1989
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-21569-2
DOI
10.1007/978-3-662-21569-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 120
Topics