Hybrid steepest-descent methods with a countable family of nonexpansive mappings for variational inequalities in Hilbert spaces. (English) Zbl 1277.47076
In this paper, the hybrid steepest-descent method for solving the variational inequality which was introduced by I. Yamada [Amsterdam: North-Holland/ Elsevier. Stud. Comput. Math. 8, 473–504 (2001; Zbl 1013.49005)] is again generalized. The authors establish a new hybrid steepest-descent method with two countable families of nonexpansive mappings for solving the variational inequality in Hilbert space without assuming the consistency condition on the fixed point sets of the nonexpansive mappings. They prove that the iterative sequence strongly converges to a unique solution of the variational inequality. Moreover, applications to constrained generalized pseudoinverses are also presented.
Reviewer: Narin Petrot (Phitsanulok)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
Citations:
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