Adaptive Proximal Method for Variational Inequalities

TL;DR

This paper introduces an adaptive proximal method for solving variational inequalities with Lipschitz and Holder-continuous fields, providing iteration estimates and generalizations for broader applicability.

Contribution

It presents a novel adaptive proximal algorithm for variational inequalities, including extensions to Holder-continuous fields, with iteration complexity analysis.

Findings

Provides iteration estimates for solution accuracy.

Generalizes the method to Holder-continuous fields.

Demonstrates effectiveness of the adaptive approach.

Abstract

A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A generalization of the method under consideration to the case of a Holder-continuous field is considered.