Open AccessALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS
Author(s) -
Ya. I. Vedel,
С. В. Денисов,
V. V. Semenov
Publication year - 2020
Publication title -
žurnal občislûvalʹnoï ta prikladnoï matematiki
Language(s) - English
Resource type - Journals
eISSN - 2706-9699
pISSN - 2706-9680
DOI - 10.17721/2706-9699.2020.1.02
Subject(s) - variational inequality , lipschitz continuity , mathematics , monotone polygon , solution set , mathematical optimization , iterative method , convergence (economics) , regularization (linguistics) , set (abstract data type) , computer science , mathematical analysis , geometry , artificial intelligence , economics , programming language , economic growth
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.