# Some adaptive proximal method for a special class of variational inequalities and related problems

## TL;DR

This paper introduces an adaptive proximal method tailored for a specific class of variational inequalities and related problems, providing iteration estimates to ensure solution quality.

## Contribution

It proposes a novel adaptive proximal algorithm for mixed variational inequalities and composite saddle problems, with theoretical iteration bounds.

## Key findings

- The method effectively solves the targeted variational inequalities.
- Iteration estimates are provided for achieving desired solution accuracy.
- The approach enhances existing algorithms for related problems.

## Abstract

An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the necessary number of iterations are obtained to achieve a given quality of the solution.