# Universal methods for variational inequalities: deterministic and stochastic cases

Source: [Universal methods for variational inequalities: deterministic and stochastic cases](<https://www.sota2.com/research/paper/68fa5c5f1e209131ce9d0612>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:35:30.112Z

Authors: Anton Klimza, Alexander Gasnikov, Fedor Stonyakin, Mohammad Alkousa

Published: 2024-07-17T14:18:21.000Z

## Abstract

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder 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 Holder 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 Holder exponent and Holder 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2407.17519>)

[PDF](<https://arxiv.org/pdf/2407.17519.pdf>)