# Bregman Golden Ratio Algorithms for Variational Inequalities

arXiv: https://arxiv.org/abs/2208.05102 · HTML: https://mlsanity.com/paper/2208.05102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2022.

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

- [A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis](https://mlsanity.com/paper/2603.12838/) (2026)

## Abstract (arXiv)

Variational inequalities provide a framework through which many optimisation problems can be solved, in particular, saddle-point problems. In this paper, we study modifications to the so-called Golden RAtio ALgorithm (GRAAL) for variational inequalities -- a method which uses a fully explicit adaptive step-size, and provides convergence results under local Lipschitz assumptions without requiring backtracking. We present and analyse two Bregman modifications to GRAAL: the first uses a fixed step-size and converges under global Lipschitz assumptions, and the second uses an adaptive step-size rule. Numerical performance of the former method is demonstrated on a bimatrix game arising in network communication, and of the latter on two problems, namely, power allocation in Gaussian communication channels and N-person Cournot completion games. In all of these applications, an appropriately chosen Bregman distance simplifies the projection steps computed as part of the algorithm.