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Nonsmooth analysis of eigenvalues: A summary

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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

  1. Ashbaugh, M.S. andBenguria, R.D.,Proof of the Payne-Pólya-Weinberger conjecture, Bulletin of American Mathematical Society,25 (1991), 19–29.

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  2. Clarke, F.H., Optimization and nonsmooth analysis, Wiley, New York, 1983.

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  3. Horn, R.A. andJohnson, C., Matrix analysis, Cambridge University Press, Cambridge, U.K., 1985.

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  4. Lewis, A.S., Nonsmooth analysis of eigenvalues, forthcoming.

  5. Lewis, A.S. andOverton, M.L.,Eigenvalue optimization, Acta Numerica, 1996, to appear.

  6. Rockafellar, R.T. andWets, R.J.B., Variational analysis, 1996, to appear.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Adrian S. Lewis

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  1. Adrian S. Lewis
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conferenza tenuta il 25 marzo 1996

The author wishes to thank the University of Milan, and in particular Dr Roberto Lucchetti, for their kind hospitality during the writing of this article. This research was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Lewis, A.S. Nonsmooth analysis of eigenvalues: A summary. Seminario Mat. e. Fis. di Milano 66, 33–41 (1996). https://doi.org/10.1007/BF02925352

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  • DOI: https://doi.org/10.1007/BF02925352

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