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Regularization and iteration methods for a class of monotone variational inequalities. (English) Zbl 1179.58008
Summary: We consider the monotone variational inequality of finding x * C such that (I-T)x * ,x-x * 0 for xC, where C is a closed convex subset of a real Hilbert space and T is a nonexpansive self-mapping of C. Techniques of nonexpansive mappings are applied to regularize this variational inequality. The regularized solutions and an iteration process are shown to converge in norm to a solution of this variational inequality.
MSC:
58E35Variational inequalities (global problems)
47H09Mappings defined by “shrinking” properties
65J15Equations with nonlinear operators (numerical methods)