# Multilevel Bregman Proximal Gradient Descent

arXiv: https://arxiv.org/abs/2506.03950 · HTML: https://mlsanity.com/paper/2506.03950/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2025.

## Built on by (most cited first, 2 of 2)

- [Sparse Training of Neural Networks based on Multilevel Mirror Descent](https://mlsanity.com/paper/2602.03535/) (2026)
- [Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2606.24567/) (2026)

## Abstract (arXiv)

We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical multilevel optimization framework (MGOPT) to handle Bregman-based geometries and constrained domains. We provide a rigorous analysis of ML BPGD for multiple coarse levels and establish a global linear convergence rate. We demonstrate the effectiveness of ML BPGD in the context of image reconstruction, providing theoretical guarantees for the well-posedness of the multilevel framework and validating its performance through numerical experiments.