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Journal of Automation and Information Sciences

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ISSN Печать: 1064-2315

ISSN Онлайн: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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Modified Extragradient Method with Bregman Divergence for Variational Inequalities

Том 50, Выпуск 8, 2018, pp. 26-37
DOI: 10.1615/JAutomatInfScien.v50.i8.30
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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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ЦИТИРОВАНО В
  1. 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

  2. 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

  3. 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

  4. Vedel Yana, Semenov Vladimir, Adaptive Extraproximal Algorithm for the Equilibrium Problem in Hadamard Spaces, in Optimization and Applications, 12422, 2020. Crossref

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

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