Convex Functions, Monotone Operators and Differentiability
Robert R. Phelps
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.
카테고리:
년:
1989
판:
1
출판사:
Springer
언어:
english
페이지:
123
ISBN 10:
3540507353
ISBN 13:
9783540507352
파일:
DJVU, 869 KB
IPFS:
,
english, 1989
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