Algorithm for Variational Inequality Problem Over the Set of Solutions the Equilibrium Problems

Vedel, Ya. I.; Денисов, С. В.; Semenov, V. V.

doi:10.17721/2706-9699.2020.1.02

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Показано, що запропонованi алгоритми можна застосувати до монотонних дворiвневих варiацiйних нерiвностей в гiльбертових просторах. Попереднi результати опублiковано в роботах [15,16].…”

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Two-Level Problems and Two-Stage Proximal Algorithm

Semenov¹,

Vedel²,

Денисов³

2021

JNAM

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In this paper, a two-level problem is considered: a variational inequality on the set of solutions to the equilibrium problem. An example of such a problem is the search for the normal Nash equilibrium. To solve this problem, two algorithms are proposed. The first combines the ideas of a two-step proximal method and iterative regularization. And the second algorithm is an adaptive version of the first with a parameter update rule that does not use the values of the Lipschitz constants of the bifunction. Theorems on strong convergence of algorithms are proved for monotone bifunctions of Lipschitz type and strongly monotone Lipschitz operators. It is shown that the proposed algorithms can be applied to monotone two-level variational inequalities in Hilbert spaces.

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