# An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization

arXiv: https://arxiv.org/abs/2010.12133 · HTML: https://mlsanity.com/paper/2010.12133/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 13 of 13)

- [Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applications](https://mlsanity.com/paper/2209.12638/) (2022)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [Deep Nonnegative Matrix Factorization with Beta Divergences](https://mlsanity.com/paper/2309.08249/) (2023)
- [Block Majorization Minimization with Extrapolation and Application to β-NMF](https://mlsanity.com/paper/2401.06646/) (2024)
- [Maximum-Volume Nonnegative Matrix Factorization](https://mlsanity.com/paper/2602.04795/) (2026)
- [Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints](https://mlsanity.com/paper/2201.07657/) (2022)
- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)
- [A Linearized Alternating Direction Multiplier Method for Federated Matrix Completion Problems](https://mlsanity.com/paper/2503.12733/) (2025)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)
- [Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2601.09316/) (2026)
- [An Inertial Block Proximal Linearized Method with Adaptive Momentum for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2608.05502/) (2026)
- [Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2609.39301/) (2026)

## Abstract (arXiv)

In this paper, we introduce TITAN, a novel inerTIal block majorizaTion minimizAtioN framework for non-smooth non-convex optimization problems. To the best of our knowledge, TITAN is the first framework of block-coordinate update method that relies on the majorization-minimization framework while embedding inertial force to each step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal gradient methods as special cases. By choosing various surrogate functions, such as proximal, Lipschitz gradient, Bregman, quadratic, and composite surrogate functions, and by varying the extrapolation operator, TITAN produces a rich set of inertial block-coordinate update methods. We study sub-sequential convergence as well as global convergence for the generated sequence of TITAN. We illustrate the effectiveness of TITAN on two important machine learning problems, namely sparse non-negative matrix factorization and matrix completion.