Convex Functions, Monotone Operators and Differentiability

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 thi...

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Main Author: Phelps, Robert R.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1989, 1989
Edition:1st ed. 1989
Series:Lecture Notes in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Summary: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
Physical Description:XII, 120 p online resource
ISBN:9783662215692