Nonsmooth analysis of eigenvalues: A summary

  • Adrian S. Lewis
Conferenze

Abstract

I outline a unified approach to characterizing Fréchet, limiting Fréchet, and Clarke subgradients of an arbitrary function of the eigenvalues of a real symmetric matrix. In particular, I compute various subdifferentials of thek'th largest eigenvalue. This paper summarizes the results and techniques presented in detail in [4].

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References

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    Ashbaugh, M.S. andBenguria, R.D.,Proof of the Payne-Pólya-Weinberger conjecture, Bulletin of American Mathematical Society,25 (1991), 19–29.MATHCrossRefMathSciNetGoogle Scholar
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    Clarke, F.H., Optimization and nonsmooth analysis, Wiley, New York, 1983.MATHGoogle Scholar
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    Horn, R.A. andJohnson, C., Matrix analysis, Cambridge University Press, Cambridge, U.K., 1985.MATHGoogle Scholar
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    Lewis, A.S., Nonsmooth analysis of eigenvalues, forthcoming.Google Scholar
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    Lewis, A.S. andOverton, M.L.,Eigenvalue optimization, Acta Numerica, 1996, to appear.Google Scholar
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    Rockafellar, R.T. andWets, R.J.B., Variational analysis, 1996, to appear.Google Scholar

Copyright information

© Birkhäuser-Verlag 1998

Authors and Affiliations

  • Adrian S. Lewis
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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