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ISSN 打印: 1064-2315

ISSN 在线: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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A Strongly Convergent Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

卷 47, 册 7, 2015, pp. 31-46
DOI: 10.1615/JAutomatInfScien.v47.i7.40
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摘要

The regularized modified extragradient method with dynamic rule for finding the step size for solving variational inequalities with monotone operators acting in a Hilbert space is presented. In addition the variants of this method for variational inequalities and operator equations with a priori information about solution, which is given as the set of fixed points of quasinonexpanding operator, are also considerd. Theorems of methods strong convergence without any Lipschitzian continuity assumption on operators are proved.

对本文的引用
  1. Lyashko Sergey I., Semenov Vladimir V., A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming, in Optimization and Its Applications in Control and Data Sciences, 115, 2016. Crossref

  2. Semenov Vladimir V., A variant of mirror descent method for solving variational inequalities, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017. Crossref

  3. Semenov V. V., A Version of the Mirror descent Method to Solve Variational Inequalities*, Cybernetics and Systems Analysis, 53, 2, 2017. Crossref

  4. Semenov V.V., A new modified extragradient method with Bregman divergence, Reports of the National Academy of Sciences of Ukraine, 8, 2018. Crossref

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  6. Semenov V.V., Convergence of inertial hybrid splitting algorithms, Reports of the National Academy of Sciences of Ukraine, 12, 2018. Crossref

  7. 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

  8. 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

  9. Migórski Stanisław, Fang Changjie, Zeng Shengda, A new modified subgradient extragradient method for solving variational inequalities, Applicable Analysis, 100, 1, 2021. Crossref

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

  11. 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

  12. Семенов В.В., Сірик Д.С., Харьков О.С., Збіжність методу операторної екстраполяції, Reports of the National Academy of Sciences of Ukraine, 4, 2021. Crossref

  13. 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

  14. Vedel Ya. I., Denisov S. V., Semenov V. V., An Adaptive Algorithm for the Variational Inequality Over the Set of Solutions of the Equilibrium Problem, Cybernetics and Systems Analysis, 57, 1, 2021. Crossref

  15. 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

  16. 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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