On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization
Optimization and Control
2026-03-31 v1
Abstract
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially simplified proof compared to previous ones. It allows us to enlarge the set of admissible step-sizes. Building on this general reformulation, we also prove the convergence of a doubly proximal algorithm in the weakly convex-strongly concave setting. Finally, we show how this new result opens the way to new applications of min-max optimization algorithms for solving regularized imaging inverse problems with neural networks in a plug-and-play manner.
Cite
@article{arxiv.2603.28484,
title = {On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization},
author = {Guido Tapia-Riera and Camille Castera and Nicolas Papadakis},
journal= {arXiv preprint arXiv:2603.28484},
year = {2026}
}