Universal methods for variational inequalities: Deterministic and stochastic cases

Anton Klimza, Alexander Gasnikov, Fedor Stonyakin and Mohammad Alkousa

Chaos, Solitons & Fractals, 2024, vol. 187, issue C

Abstract: In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Hölder-continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the oracle’s noise (in the stochastic setting of the problem) but also to the Hölder continuity of the operator without having prior knowledge of either the problem class or the nature of the operator information. We analyzed the proposed algorithms in both deterministic and stochastic settings and obtained estimates for the required number of iterations to achieve a given quality of a solution to the variational inequality. We showed that, without knowing the Hölder exponent and Hölder constant of the operators, the proposed algorithms have the least possible in the worst-case sense complexity for the considered class of variational inequalities. We also compared the resulting stochastic algorithm with other popular optimizers for the task of image classification.

Keywords: Variational inequality; Hölder continuous operator; Universal method; Proximal mirror method; Saddle point problem; Image classification (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009706

DOI: 10.1016/j.chaos.2024.115418

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