Адаптивний метод операторної екстраполяції: Fìz.-mat. model. ìnf. tehnol. 2021, 33:143-147

• Date: 2021
• Main Authors: Semenov, Volodymyr, Siryk, Dmytro, Kharkov, Oleh
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: варіаційна нерівність; операторна екстраполяція; збіжність; дивергенція Брегмана
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/218
• Journal Title: Physico-mathematical modeling and informational technologies

This paper is devoted to the study of nоvel algorithm with Bregman projection for solving variational inequalities in Hilbert space. Proposed algorithm is an adaptive version of the operator extrapolation method, where the used rule for updating the step size does not require knowledge of Lipschitz constants and the calculation of operator values at additional points. An attractive feature of the algorithm is only one computation at the iterative step of the Bregman projection onto the feasible set. References Gidel, G., Berard, H., Vincent, P., Lacoste-Julien, S. (2018). A Variational Inequality Perspective on Generative Adversarial Networks. arXiv preprint arXiv:1802.10551. Semenov, V. V. (2017). A Version of the Mirror descent Method to Solve Variational Inequalities. Cybernetics and Systems Analysis, 53(2), 234-243. DOI https://doi.org/10.1007/s10559-017-9923-9 Malitsky, Y., Tam, M. K. (2020). A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity. SIAM Journal on Optimization, 30(2), 1451-1472. DOI https://doi.org/10.1137/18m1207260 Denisov, S. V., Semenov, V. V., Stetsyuk, P. I. (2019). Bregman Extragradient Method with Monotone Rule of Step Adjustment. Cybernetics and Systems Analysis, 55(3), 377-383. DOI https://doi.org/10.1007/s10559-019-00144-5 Beck, A. (2017). First-Order Methods in Optimization. – Philadelphia: Society for Industrial and Applied Mathematics.