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.
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Acknowledgment
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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Dedicated to the memory of Professor George Isac
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Wolkowicz, H. (2010). Generating Eigenvalue Bounds Using Optimization. In: Pardalos, P., Rassias, T., Khan, A. (eds) Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0158-3_29
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DOI: https://doi.org/10.1007/978-1-4419-0158-3_29
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