A Bregman firmly nonexpansive proximal operator for baryconvex optimization

Mastane Achab

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arXiv · 2411.00928

A Bregman firmly nonexpansive proximal operator for baryconvex optimization

Mastane Achab

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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.

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Mastane Achab. 2024-11-01. A Bregman firmly nonexpansive proximal operator for baryconvex optimization. https://arxiv.org/abs/2411.00928

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