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Stability under perturbations of some condition numbers in optimization

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Abstract

The behavior of condition numbers for free optimization problems under perturbations is considered in the infinite-dimensional setting. Semicontinuity properties via distance to ill-conditioning are obtained. Convergence theorems of the condition numbers are proved under variational convergence of the perturbed problems and suitable behavior of the gradients of the corresponding functionals. The particular case of convex quadratic forms is presented.

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Authors and Affiliations

  1. DIMA, Università di Genova, via Dodecaneso 35, 16146, Genova, Italy

    Tullio Zolezzi

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  1. Tullio Zolezzi
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Correspondence to Tullio Zolezzi.

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Dedicated to A. Auslender for his 65th birthday.

Work partially supported by MURST.

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Zolezzi, T. Stability under perturbations of some condition numbers in optimization. Math. Program. 116, 579–593 (2009). https://doi.org/10.1007/s10107-007-0135-3

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  • DOI: https://doi.org/10.1007/s10107-007-0135-3

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