Generating Eigenvalue Bounds Using Optimization

  • Henry Wolkowicz
Part of the Springer Optimization and Its Applications book series (SOIA, volume 35)


This paper illustrates how optimization can be used to derive known and new theoretical results about perturbations of matrices and sensitivity of eigenvalues. More specifically, the Karush–Kuhn–Tucker conditions, the shadow prices, and the parametric solution of a fractional program are used to derive explicit formulae for bounds for functions of matrix eigenvalues.


Lagrange Multiplier Large Eigenvalue Shadow Price Fractional Programming Shadow Prex 


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Research supported by The Natural Sciences and Engineering Research Council of Canada. The author thanks Wai Lung Yeung for his help in correctiong many statements in the paper.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Henry Wolkowicz
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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