# Proximal extrapolated gradient methods for variational inequalities

arXiv: https://arxiv.org/abs/1601.04001 · HTML: https://mlsanity.com/paper/1601.04001/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [Generalized Optimistic Methods for Convex-Concave Saddle Point Problems](https://mlsanity.com/paper/2202.09674/) (2022)
- [Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalities](https://mlsanity.com/paper/2604.07662/) (2026)

## Abstract (arXiv)

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require Lipschitz-continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when operator is affine our linesearch becomes very simple, namely, it needs only vector-vector multiplication. For all our methods we establish the ergodic convergence rate. Although the proposed methods are very general, sometimes they may show much better performance even for optimization problems. The reason for this is that they often can use larger stepsizes without additional expensive computation.