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Convex Functions, Monotone Operators and Differentiability

  • Book
  • © 1989

Overview

Authors:
  1. Robert R. Phelps

    1. Department of Mathematics GN-50, University of Washington, Seattle, USA

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1364)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-IX
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  2. Convex functions on real Banach spaces

    • Robert R. Phelps
    Pages 1-16

  3. Monotone operators, subdifferentials and Asplund spaces

    • Robert R. Phelps
    Pages 17-39

  4. Lower semicontinuous convex functions

    • Robert R. Phelps
    Pages 40-63

  5. A smooth variational principle and more about Asplund spaces

    • Robert R. Phelps
    Pages 64-71

  6. Asplund spaces, the Radon-Nikodym property and optimization

    • Robert R. Phelps
    Pages 72-89

  7. Gateaux differentiability spaces

    • Robert R. Phelps
    Pages 90-96

  8. A generalization of monotone operators: Usco maps

    • Robert R. Phelps
    Pages 97-103

  9. Notes and Remarks

    • Robert R. Phelps
    Pages 104-107

  10. Back Matter

    Pages 108-118
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics GN-50, University of Washington, Seattle, USA

    Robert R. Phelps

Bibliographic Information

  • Book Title: Convex Functions, Monotone Operators and Differentiability

  • Authors: Robert R. Phelps

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-21569-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • eBook ISBN: 978-3-662-21569-2Published: 11 December 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 120

  • Topics: Analysis

  • Industry Sectors: Energy, Utilities & Environment, Engineering, IT & Software

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