# Popov Mirror-Prox for solving Variational Inequalities

arXiv: https://arxiv.org/abs/2404.00635 · HTML: https://mlsanity.com/paper/2404.00635/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes](https://mlsanity.com/paper/2601.20076/) (2026)

## Abstract (arXiv)

We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its implementation with Popov method updates. We provide convergence rate analysis of our proposed method for a monotone VI with a Lipschitz continuous mapping. We establish a convergence rate of O(1/t), in terms of the number t of iterations, for the dual gap function. Simulations on a two player matrix game corroborate our findings.