Abstract
This paper is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Based on the recently proposed proximal version of the extragradient method for this class of problems, we study in detail the method with adaptively selected parameter values. The rate of convergence of this method is estimated. The result is generalized to the class of variational inequalities with relatively strongly monotone δ-generalized smooth operators. For the ridge regression problem and variational inequality associated with box-simplex games, numerical experiments are carried out to demonstrate the effectiveness of the proposed technique for adaptive parameter selection during the execution of the algorithm.
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Funding
The work carried out in Section 2 was partially supported by the Priority 2030 strategic academic leadership program, agreement no. 075-02-2021-1316 (dated September 9, 2021). The work carried out in Section 4 was supported by the grant from the President of the Russian Federation for the state support of leading scientific schools, grant no. NSh775.2022.1.1.
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Translated by Yu. Kornienko
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Ablaev, S.S., Stonyakin, F.S., Alkousa, M.S. et al. Adaptive Methods for Variational Inequalities with Relatively Smooth and Reletively Strongly Monotone Operators. Program Comput Soft 49, 485–492 (2023). https://doi.org/10.1134/S0361768823060026
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DOI: https://doi.org/10.1134/S0361768823060026