Mathematical Programming

, Volume 24, Issue 1, pp 225–228 | Cite as

A note on the existence of subgradients

  • J. M. Borwein
Short Communication

Abstract

We describe an apparently novel way of constructing the subgradient of a convex function defined on a finite dimensional vector space.

Key words

Convex Function Subgradient Max-formula 

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References

  1. [1]
    M.S. Bazaraa and C.M. Shetty,Nonlinear programming. Theory and algorithms (Wiley, New York, 1979).Google Scholar
  2. [2]
    J.M. Borwein, “Subgradients of convex operators”, Research Report 82-3, Department of Mathematics, Carnegie-Mellon University (Pittsburgh, PA, 1982).Google Scholar
  3. [3]
    R.B. Holmes,Geometric functional analysis and its applications (Springer, New York, 1975).Google Scholar
  4. [4]
    D.G. Luenberger,Optimization by vector space methods (Wiley, New York, 1969).Google Scholar
  5. [5]
    A.W. Roberts and D.E. Varberg,Convex functions (Academic Press, New York, 1973).Google Scholar
  6. [6]
    R.T. Rockafellar,Convex analysis (Princeton University Press, Princeton, NJ, 1970).Google Scholar
  7. [7]
    J.F. Shapiro,Mathematical programming: Structures and algorithms (Wiley, New York, 1979).Google Scholar
  8. [8]
    J. Stoer and C. Witzgall,Convexity and optimization in finite dimensions I (Springer, Berlin, 1970).Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1982

Authors and Affiliations

  • J. M. Borwein
    • 1
    • 2
  1. 1.Carnegie-Mellon UniversityPittsburghUSA
  2. 2.Dalhousie UniversityHalifaxCanada

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