ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS
DOI:
https://doi.org/10.17721/2706-9699.2020.1.02Keywords:
bilevel problem, variational inequality, equilibrium problem, two-stage proximal algorithm, iterative regularization, strong convergenceAbstract
In this paper, we consider bilevel problem: variational inequality problem over the set of solutions the equilibrium problems. To solve this problem, an iterative algorithm is proposed that combines the ideas of a two-stage proximal method and iterative regularization. For monotone bifunctions of Lipschitz type and strongly monotone Lipschitz continuous operators, the theorem on strong convergence of sequences generated by the algorithm is proved.
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