A projection and contraction method with adaptive step sizes for solving bilevel pseudo-monotone variational inequality problems. (English) Zbl 07558497
Summary: In this paper, we propose a single projection method for finding a solution of the bilevel pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm requires only one projection onto the feasible set. Also, we prove strong convergence theorems of the proposed method under mild conditions, which improve some related results in the literature. Finally, we present some numerical experiments to show the efficiency and advantages of the proposed algorithm.
MSC:
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47J05 | Equations involving nonlinear operators (general) |
| 47J25 | Iterative procedures involving nonlinear operators |
Keywords:
contraction and projection method; bilevel variational inequality problem; pseudo-monotone mappingReferences:
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