Algorithm for solving variational inequalities with relatively strongly monotone operators

TL;DR

This paper introduces a new algorithm based on the Mirror Prox method for solving variational inequalities involving relatively strongly monotone and smooth operators, extending existing methods to a broader class of problems.

Contribution

It proposes an analogue of the Mirror Prox method tailored for variational inequalities with relatively strongly monotone operators under relative smoothness assumptions.

Findings

The algorithm effectively handles non-smooth operators.

It extends the applicability of Mirror Prox to new problem classes.

The method demonstrates convergence under relative strong monotonicity.

Abstract

Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness and relative strong monotonicity of the operator.