mlsanityData to 7 Oct 2026

Block Alternating Bregman Majorization Minimization with Extrapolation

arXiv 2107.04395 ↗First posted 9 Jul 2021math.OC cs.NA eess.SPcited by 4

Not on the map. Why?

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 12 of its 39 references that are in the map. First posted on arXiv 9 Jul 2021.

Builds on

12 of 39 references.

References · 12

  1. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  2. 2017Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problemscited by 40
  3. 2017First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problemscited by 37
  4. 2014A globally convergent algorithm for nonconvex optimization based on block coordinate updatecited by 29
  5. 2020Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergencecited by 17
  6. 2019Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimizationcited by 12
  7. 2013Hierarchical Clustering of Hyperspectral Images using Rank-Two Nonnegative Matrix Factorizationcited by 11
  8. 2016Unifying abstract inexact convergence theorems and block coordinate variable metric iPianocited by 10
  9. 2019Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorizationcited by 7
  10. 2014A fast patch-dictionary method for whole image recoverycited by 5
  11. 2019Beyond Alternating Updates for Matrix Factorization with Inertial Bregman Proximal Gradient Algorithmscited by 5
  12. 2020A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorizationcited by 4

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 1; 2025: 2.

4 papers.

  1. 2025An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decompositioncited by 4
  2. 2022Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraintscited by 0
  3. 2024Matrix Completion via Nonsmooth Regularization of Fully Connected Neural Networkscited by 0
  4. 2025Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learningcited by 0