A Bregman firmly nonexpansive proximal operator for baryconvex optimization
Optimization and Control
2025-04-14 v3 Machine Learning
Abstract
We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries; and that its fixed points are given by the critical points of a certain nonconvex function. Finally, we derive the associated continuous flows.
Cite
@article{arxiv.2411.00928,
title = {A Bregman firmly nonexpansive proximal operator for baryconvex optimization},
author = {Mastane Achab},
journal= {arXiv preprint arXiv:2411.00928},
year = {2025}
}