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Three-step relaxed hybrid steepest-descent methods for variational inequalities. (English) Zbl 1231.49004
Summary: The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.

MSC:
49J30Optimal solutions belonging to restricted classes (existence)
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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