The behavior of condition numbers for free optimization problems under perturbations is considered in the innite - 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.
Stability under perturbations of some condition numbers in optimization.
ZOLEZZI, TULLIO
2009-01-01
Abstract
The behavior of condition numbers for free optimization problems under perturbations is considered in the innite - 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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