Generating Eigenvalue Bounds Using Optimization

Henry Wolkowicz
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Henry Wolkowicz: University of Waterloo

Chapter Chapter 29 in Nonlinear Analysis and Variational Problems, 2010, pp 465-490 from Springer

Abstract: Abstract 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.

Keywords: Lagrange Multiplier; Large Eigenvalue; Shadow Price; Fractional Programming; Shadow Prex (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0158-3_29

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DOI: 10.1007/978-1-4419-0158-3_29

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