ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEM OVER THE SET OF SOLUTIONS THE EQUILIBRIUM PROBLEMS | Zendy

Ya. I. Vedel | Zendy; С. В. Денисов | Zendy; V. V. Semenov | Zendy

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ALGORITHM 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 -

journal of numerical and applied mathematics

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.

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