Author:
Kovalenko O. Yu., ,Semenov V. V.,Kharkov O. S., ,
Abstract
The article considers variational inequalities with operators acting in a Hilbert space. For these problems, variants of the Operator Extrapolation method have been proposed and studied. A sub-linear efficiency estimate for the gap function is proved. The strong convergence of the Operator Extrapolation method for variational inequalities with uniformly monotone operators is proved. The linear rate of convergence of the Operator Extrapolation method for variational inequalities with operators satisfying the generalized strong monotonicity condition is proved. An adaptive version of the algorithm is proposed. Regularized variants of the algorithm are proposed and theorems on their strong convergence are proved.
Publisher
Taras Shevchenko National University of Kyiv
Reference34 articles.
1. 1. Semenov V.V., Kharkov O.S. Extrapolation from the past method for variational inequalities in Hilbert space. Journal of Numerical and Applied Mathematics. 2023. No 2. P. 52-82. https://doi.org/10.17721/2706-9699.2023.2.04
2. 2. Malitsky Y., Tam M.K. A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity. SIAM J. on Optim. 2020. Vol. 30. P. 1451-1472
3. 3. Gidel G., Berard H., Vincent P., Lacoste-Julien S. A Variational Inequality Perspective on Generative Adversarial Networks. arXiv preprint arXiv:1802.10551.2018.
4. 4. Mokhtari A., Ozdaglar A., Pattathil S. A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: proximal point approach. arXiv preprint arXiv:1901.08511.2019.
5. 5. Mokhtari A., Ozdaglar A., Pattathil S. Convergence rate of O(1/k) for optimistic gradient and extra-gradient methods in smooth convex-concave saddle point problems. arXiv preprint arXiv:1906.01115.2020.