Convex Functions, Monotone Operators and Differentiability

Released on by Robert R. Phelps
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  • Convex Functions, Monotone Operators and Differentiability Book Detail

  • Author : Robert R. Phelps
  • Release Date : 2013-12-11
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 125
  • ISBN 13 : 3662215691
  • File Size : 34,34 MB
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Convex Functions, Monotone Operators and Differentiability by Robert R. Phelps PDF Summary

Book 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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Convex Functions

Convex Functions

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Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and appl