Tikhonov regularization under epi-convergent perturbations
Global optimization problems in a Banach space with perturbed data are considered. At each stage an approximate minimization is performed by applying Tikhonov regularization to every perturbed problems. Known results show that Tikhonov regularization provides strongly convergent minimizing sequences (up to subsequences) in case of perturbed data converging uniformly. In this paper, the author generalizes those results to nonconvex problems in case of epi-convergent perturbations of the original problem, making use of the notion of epi-distance, and applies the new results to ill-posed problems under perturbations. In the end, a quantitative estimate of the rate of convergence of the regularization assuming convexity of the data is obtained.
scientific article; zbMATH DE number 1846795