# Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems

arXiv: https://arxiv.org/abs/1512.09302 · HTML: https://mlsanity.com/paper/1512.09302/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2015.

## Built on by (most cited first, 3 of 3)

- [Distributed Sparse Regression via Penalization](https://mlsanity.com/paper/2111.06530/) (2021)
- [Network Tomography with Path-Centric Graph Neural Network](https://mlsanity.com/paper/2502.16430/) (2025)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)

## Abstract (arXiv)

In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a threshold such that if the extrapolation coefficients are chosen below this threshold, then the sequence generated converges R-linearly to a stationary point of the problem. Moreover, the corresponding sequence of objective values is also R-linearly convergent. In addition, the threshold reduces to 1 for convex problems and, as a consequence, we obtain the R-linear convergence of the sequence generated by FISTA with fixed restart. Finally, we present some numerical experiments to illustrate our results.