# A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization

arXiv: https://arxiv.org/abs/2003.03963 · HTML: https://mlsanity.com/paper/2003.03963/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [Block Alternating Bregman Majorization Minimization with Extrapolation](https://mlsanity.com/paper/2107.04395/) (2021)
- [Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization](https://mlsanity.com/paper/2104.12289/) (2021)
- [On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem](https://mlsanity.com/paper/2606.08291/) (2026)
- [Matrix Completion via Nonsmooth Regularization of Fully Connected Neural Networks](https://mlsanity.com/paper/2403.10232/) (2024)

## Abstract (arXiv)

We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We prove that the sequence generated by BIBPA subsequentially converges to critical points of the objective under standard assumptions, and globally converges when the objective function is additionally assumed to satisfy the Kurdyka-Lojasiewicz (KL) property. We also provide the convergence rate when the objective satisfies the Lojasiewicz inequality. We apply BIBPA to the symmetric nonnegative matrix tri-factorization (SymTriNMF) problem, where we propose kernel functions for SymTriNMF and provide closed-form solutions for subproblems of BIBPA.