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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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Modified Extragradient Method with Bregman Divergence for Variational Inequalities

卷 50, 册 8, 2018, pp. 26-37
DOI: 10.1615/JAutomatInfScien.v50.i8.30
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摘要

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

参考文献
  1. Konnov I.V., Combined relaxation methods for variational inequalities, Springer-Verlag, Berlin-Heidelberg-New York, 2001.

  2. Korpelevich G.M., Extragradient method for finding saddle points and other problems, Ekonomika i matematicheskie metody, 1976, 12, No. 4, 747–756.

  3. Khobotov E.N., On modification of extragradient method for solving variational inequalities and some optimization problems, Zhurnal vychislitelnoy matematiki i matematicheskoy fiziki, 1987, No. 10, 1462–1473.

  4. Tseng P., A modified forward-backward splitting method for maximal monotone mappings, SIAM Journal on Control and Optimization, 2000, 38, 431–446.

  5. Semenov V.V., Hybrid splitting methods for systems of operator inclusions with monotone operators, Kibernetika i sistemnyi analiz, 2014, No. 5, 104–112.

  6. Semenov V.V., Strongly converging splitting method for systems of operator inclusions with monotone operators, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal “Problemy upravleniya i informatiki”, 2014, No. 3, 22–32.

  7. Lyashko S.I., Semenov V.V., A new two-step proximal algorithm of solving the problem of equilibrium programming, In: Goldengorin B. (ed.) Optimization and its Applications in Control and Data Sciences, Springer Optimization and its Applications, Cham, Springer, 2016, 115, 315–325.

  8. Censor Y., Gibali A., Reich S., The subgradient extragradient method for solving variational inequalities in Hilbert space, Journal of Optimization Theory and Applications, 2011, 148, 318–335.

  9. 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.

  10. 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.

  11. 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.

  12. Bregman L.M., Relaxation method for finding a common point of convex sets and its application to solving problems of convex programming, Zhurnal vychislit. matematiki i mat. fiziki, No. 3, 620–631.

  13. Beck A., Teboulle M., Mirror descent and nonlinear projected subgradient methods for convex optimization, Operations Research Letters, 2003, 31, No. 3, 167–175.

  14. Nemirovski A., Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems, SIAM Journal on Optimization, 2004, 15, 229–251.

  15. Auslender A., Teboulle M., Interior projection-like methods for monotone variational inequalities, Mathematical Programming, 2005, 104, No. 1, 39–68.

  16. Nesterov Yu., Dual extrapolation and its applications to solving variational inequalities and related problems, Ibid., 2007, 109, No. 2–3, 319–344.

  17. Semenov V.V., Variant of mirror descent method for variational inequalities, Kibernetika i sistemnyi analiz, 2017, No. 2, 83–93.

  18. 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.

  19. Viyugin V.V., Mathematical foundations of machine learning and forecasting [in Russian], MTSNMO, Moscow, 2018.

  20. Lorenz D.A., Schöpfer F., Wenger S., The linearized Bregman method via split feasibility problems: Analysis and Generalizations, SIAM Journal on Imaging Sciences, 2014, 7, No. 2, 1237–1262.

对本文的引用
  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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