Regularization and iteration methods for a class of monotone variational inequalities. (English) Zbl 1179.58008
Summary: We consider the monotone variational inequality of finding \(x^*\in C\) such that \(\langle(I-T)x^*, x-x^*\rangle\geq 0\) for \(x\in C\), 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:
58E35 | Variational inequalities (global problems) in infinite-dimensional spaces |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
65J15 | Numerical solutions to equations with nonlinear operators |