In this paper we study the convergence and stability in reflexive, smooth and strictly convex Banach spaces of a regularization method for variational inequalities with data perturbations. We prove that, when applied to perturbed variational inequalities with monotone, demiclosed, convex valued operators satisfying certain conditions of asymptotic growth, the regularization method we consider produces sequences which converge weakly to the minimal-norm solution of the original variational inequality, provided that the perturbed constraint sets converge to the constraint set of the original inequality in the sense of a modified form of Mosco convergence of order ≥1. If the underlying Banach space has the Kadeč-Klee property, then the sequence generated by that regularization method is strongly convergent.
Bibliographical noteFunding Information:
The work of Yakov Alber was supported in part by the KAMEA Program of the Israeli Ministry of Absorption. Dan Butnariu gratefully acknowledges the support of the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Grant No. 592/00).
- Demiclosed operator
- Fast Mosco-convergence relative to a sequence of positive real numbers
- Monotone operator
- Mosco convergence
- Regularization method
- Variational inequality
ASJC Scopus subject areas
- Applied Mathematics