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Zbl 1179.58008
Chen, Rudong; Su, Yongfu; Xu, Hong-Kun
Regularization and iteration methods for a class of monotone variational inequalities.
(English)
[J] Taiwanese J. Math. 13, No. 2B, 739-752 (2009). ISSN 1027-5487

Summary: We consider the monotone variational inequality of finding $x^*\in C$ such that $\langle(I-T)x^*, x-x^*\rangle\ge 0$ 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 2000:
*58E35 Variational inequalities (global problems)
47H09 Mappings defined by "shrinking" properties
65J15 Equations with nonlinear operators (numerical methods)

Keywords: regularization; variational inequality; nonexpansive mapping; iterative method; projection

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