Модифицированный экстраградиентный метод с дивергенцией Брэгмана для вариационных неравенств
DOI:
https://doi.org/10.32626/2308-5878.2019-19.132-137Анотація
Предложен новый метод экстраградиентного типа для решения вариационных неравенств с псевдомонотонными и липшицевыми операторами, действующими в конечномерном линейном нормированном пространстве. Доказана теорема сходимости метода и для случая монотонного оператора получены неасимптотические оценки эффективности методаПосилання
Korpelevich G. M. The extragradient method for finding saddle points and other problems. Ekonomika i Matematicheskie Metody. 1976. Vol. 12. № 4. P. 747–756.
Tseng P. A modified forward-backward splitting method for maximal monotone mappings. SIAM Journal on Control and Optimization. 2000. Vol. 38. P. 431–446.
Censor Y., Gibali A., Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. Journal of Optimization Theory and Applications. 2011. Vol. 148. P. 318–335.
Lyashko S. I., Semenov V. V., Voitova T. A. Low-cost modification of Korpelevich’s methods for monotone equilibrium problems. Cybernetics and Systems Analysis. 2011. Vol. 47. P. 631–639.
Denisov S. V., Semenov V. V., Chabak L. M. Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators. Cybernetics and Systems Analysis. 2015. Vol. 51. P. 757–765.
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. Vol. 15. P. 229–251.
Semenov V. V. A Version of the Mirror descent Method to Solve Variational Inequalities. Cybernetics and Systems Analysis. 2017. Vol. 53. P. 234–243.
##submission.downloads##
Опубліковано
Номер
Розділ
Ліцензія
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).