# An Inertial Block Proximal Linearized Method with Adaptive Momentum for Nonconvex and Nonsmooth Optimization

arXiv: https://arxiv.org/abs/2608.05502 · HTML: https://mlsanity.com/paper/2608.05502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees](https://mlsanity.com/paper/2305.03938/) (2023)
- [Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization](https://mlsanity.com/paper/1705.04925/) (2017)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Alternating proximal gradient method for sparse nonnegative Tucker decomposition](https://mlsanity.com/paper/1302.2559/) (2013)
- [Proximal Gradient Method with Extrapolation and Line Search for a Class of Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1711.06831/) (2017)
- [An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2308.12126/) (2023)
- [Inertial Accelerated Stochastic Mirror Descent for Large-Scale Generalized Tensor CP Decomposition](https://mlsanity.com/paper/2402.15771/) (2024)

## Abstract (arXiv)

In this paper, we consider a class of multiblock nonconvex nonsmooth optimization problems, which covers many applications such as the analysis of pre-earthquake anomalies and machine learning. To solve this class of problems, we propose the inertial block proximal linearized method with two-phase adaptive momentum (IBPL^+-TP). Compared to the current methods, our method possesses three main advantages: (1) it introduces a two-phase adaptive momentum strategy to effectively update the extrapolation parameters, (2) it allows using two different extrapolation points to accelerate the convergence, (3) it allows the extrapolation parameters of these two extrapolation points to be independent of and unconstrained by all other parameters. While maintaining the above advantages, we prove that our method ensures the monotonic convergence of the objective function of this class of problems, and we also prove that the sequence generated by our method globally converges to a critical point, as well as establish the convergence rate of our method. To demonstrate the effectiveness of our method, we apply it to solve two nonconvex and nonsmooth machine learning problems, namely sparse nonnegative matrix factorization with ℓ0-constraints and sparse nonnegative CP decomposition with ℓ0-constraints. The numerical experimental results on solving these problems show that our method outperforms several state-of-the-art methods.