# Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

arXiv: https://arxiv.org/abs/2401.02635 · HTML: https://mlsanity.com/paper/2401.02635/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2024.

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

- [Accelerating Spectral Clustering under Fairness Constraints](https://mlsanity.com/paper/2506.08143/) (2025)
- [Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization](https://mlsanity.com/paper/2606.28307/) (2026)

## Abstract (arXiv)

In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka--Lojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.