Mirror-Free Proximal Methods
Optimization and Control
2026-03-24 v1
Abstract
We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our method under suitable notions of relative smoothness and relative Lipschitzness, for which we introduce a relaxation of the standard Bregman divergence in terms of more general potential operators. Finally, we show how a strongly monotone variant of our method allows us to solve regularized Taylor-expansion subproblems that appear in both second- and third-order smooth min-max optimization.
Keywords
Cite
@article{arxiv.2603.20918,
title = {Mirror-Free Proximal Methods},
author = {Abhijeet Vyas and Brian Bullins},
journal= {arXiv preprint arXiv:2603.20918},
year = {2026}
}