# Block Alternating Bregman Majorization Minimization with Extrapolation

arXiv: https://arxiv.org/abs/2107.04395 · HTML: https://mlsanity.com/paper/2107.04395/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 9 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2010.01935/) (2020)
- [Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization](https://mlsanity.com/paper/1904.03537/) (2019)
- [Hierarchical Clustering of Hyperspectral Images using Rank-Two Nonnegative Matrix Factorization](https://mlsanity.com/paper/1310.7441/) (2013)
- [Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano](https://mlsanity.com/paper/1602.07283/) (2016)
- [Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization](https://mlsanity.com/paper/1908.01402/) (2019)
- [A fast patch-dictionary method for whole image recovery](https://mlsanity.com/paper/1408.3740/) (2014)
- [Beyond Alternating Updates for Matrix Factorization with Inertial Bregman Proximal Gradient Algorithms](https://mlsanity.com/paper/1905.09050/) (2019)
- [A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization](https://mlsanity.com/paper/2003.03963/) (2020)

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

- [An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decomposition](https://mlsanity.com/paper/2503.02386/) (2025)
- [Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints](https://mlsanity.com/paper/2201.07657/) (2022)
- [Matrix Completion via Nonsmooth Regularization of Fully Connected Neural Networks](https://mlsanity.com/paper/2403.10232/) (2024)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)

## Abstract (arXiv)

In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous block separable function. Although the analysis of block proximal gradient (BPG) methods for the class of block L-smooth functions have been successfully extended to Bregman BPG methods that deal with the class of block relative smooth functions, accelerated Bregman BPG methods are scarce and challenging to design. Taking our inspiration from Nesterov-type acceleration and the majorization-minimization scheme, we propose a block alternating Bregman Majorization-Minimization framework with Extrapolation (BMME). We prove subsequential convergence of BMME to a first-order stationary point under mild assumptions, and study its global convergence under stronger conditions. We illustrate the effectiveness of BMME on the penalized orthogonal nonnegative matrix factorization problem.