# On the Proximal Gradient Algorithm with Alternated Inertia

arXiv: https://arxiv.org/abs/1801.05589 · HTML: https://mlsanity.com/paper/1801.05589/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2018.

## Built on by (most cited first, 2 of 2)

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- [Robust Non-negative Proximal Gradient Algorithm for Inverse Problems](https://mlsanity.com/paper/2510.23362/) (2025)

## Abstract (arXiv)

In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions and illustrations on common regularized problems.