Two simple projection-type methods for solving variational inequalities. (English) Zbl 07152002
Summary: In this paper we study a classical monotone and Lipschitz continuous variational inequality in real Hilbert spaces. Two projection type methods, Mann and its viscosity generalization are introduced with their strong convergence theorems. Our methods generalize and extend some related results in the literature and their main advantages are: the strong convergence and the adaptive step-size usage which avoids the need to know apriori the Lipschitz constant of variational inequality associated operator. Primary numerical experiments in finite and infinite dimensional spaces compare and illustrate the behaviors of the proposed schemes.
MSC:
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 65K15 | Numerical methods for variational inequalities and related problems |
| 90C25 | Convex programming |
Keywords:
projection-type method; variational inequality; Mann-type method; viscosity method; projection and contraction methodReferences:
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