# A Bregman firmly nonexpansive proximal operator for baryconvex optimization

arXiv: https://arxiv.org/abs/2411.00928 · HTML: https://mlsanity.com/paper/2411.00928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 4 of 4)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Regularizing with Bregman-Moreau envelopes](https://mlsanity.com/paper/1705.06019/) (2017)
- [Beyond Log-Concavity: Theory and Algorithm for Sum-Log-Concave Optimization](https://mlsanity.com/paper/2309.15298/) (2023)

## Abstract (arXiv)

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.