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.


49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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