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ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337
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Modified Extragradient Method with Bregman Divergence for Variational Inequalities
Краткое описание
A new method of extragradient type for the approximate solution of variational inequalities with pseudomonotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space is proposed. This method is a modification of the subgradient extragradient algorithm using Bregman divergence instead of Euclidean distance. Like other schemes using Bregman divergence the proposed method can sometimes effectively take into account a structure of a feasible set of the problem. The theorem on the method convergence is proved and in the case of a monotone operator nonasymptotic estimates of the method effectiveness are obtained
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Lyashko S.I., Semenov V.V., Voytova T.A., Economic modification of Korpelevich method for monotone equilibrium problems, Kibernetika i sistemnyi analiz, 2011, No. 4, 146–154.
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Verlan D.A., Semenov V.V., Chaback L.M., Strongly converging modified extragradient method for variational inequalities with non-Lipschitz operators, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal “Problemy upravleniya i informatiki”, 2015, No. 4, 37–50.
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Denisov S.V., Semenov V.V., Chaback L.M., Convergence of modified extragradient method for variational inequalities with non-Lipschitz operators, Kibernetika i sistemnyi analiz, 2015, No. 5, 102–110.
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Semenov V.V., A variant of mirror descent method for solving variational inequalities. In: Polyakova, L.N. (ed.) Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017. doi: 10.1109/CNSA.2017.7974011.
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Nomirovskii D. A., Rublyov B. V., Semenov V. V., Convergence of Two-Stage Method with Bregman Divergence for Solving Variational Inequalities*, Cybernetics and Systems Analysis, 55, 3, 2019. Crossref
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Vedel Ya.I., Denisov S.V., Semenov V.V., Convergence of the Bregman extragradient method, Reports of the National Academy of Sciences of Ukraine, 5, 2019. Crossref
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Vedel Ya. I., Sandrakov G. V., Semenov V. V., An Adaptive Two-Stage Proximal Algorithm for Equilibrium Problems in Hadamard Spaces, Cybernetics and Systems Analysis, 56, 6, 2020. Crossref
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Vedel Yana, Semenov Vladimir, Adaptive Extraproximal Algorithm for the Equilibrium Problem in Hadamard Spaces, in Optimization and Applications, 12422, 2020. Crossref
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Vedel Ya. I., Sandrakov G. V., Semenov V. V., Chabak L. M., Convergence of a Two-Stage Proximal Algorithm for the Equilibrium Problem in Hadamard Spaces, Cybernetics and Systems Analysis, 56, 5, 2020. Crossref
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Vedel Yana, Semenov Vladimir, Denisov Sergey, A Novel Algorithm with Self-adaptive Technique for Solving Variational Inequalities in Banach Spaces, in Advances in Optimization and Applications, 1514, 2021. Crossref
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Semenov V. V., Denisov S. V., Kravets A. V., Adaptive Two-Stage Bregman Method for Variational Inequalities, Cybernetics and Systems Analysis, 57, 6, 2021. Crossref
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Semenov V. V., Denisov S. V., Convergence of the Method of Extrapolation from the Past for Variational Inequalities in Uniformly Convex Banach Spaces*, Cybernetics and Systems Analysis, 58, 4, 2022. Crossref
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Semenov V. V., Denisov S. V., Sandrakov G. V., Kharkov O. S., Convergence of the Operator Extrapolation Method for Variational Inequalities in Banach Spaces*, Cybernetics and Systems Analysis, 58, 5, 2022. Crossref