# Proximal Gradient Algorithm with Momentum and Flexible Parameter Restart for Nonconvex Optimization

arXiv: https://arxiv.org/abs/2002.11582 · HTML: https://mlsanity.com/paper/2002.11582/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2020.

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

- [Proximal Gradient Descent-Ascent: Variable Convergence under KL Geometry](https://mlsanity.com/paper/2102.04653/) (2021)
- [A Fast and Convergent Proximal Algorithm for Regularized Nonconvex and Nonsmooth Bi-level Optimization](https://mlsanity.com/paper/2203.16615/) (2022)

## Abstract (arXiv)

Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under parameter restart remain obscure in nonconvex optimization. In this paper, we propose a novel accelerated proximal gradient algorithm with parameter restart (named APG-restart) for solving nonconvex and nonsmooth problems. Our APG-restart is designed to 1) allow for adopting flexible parameter restart schemes that cover many existing ones; 2) have a global sub-linear convergence rate in nonconvex and nonsmooth optimization; and 3) have guaranteed convergence to a critical point and have various types of asymptotic convergence rates depending on the parameterization of local geometry in nonconvex and nonsmooth optimization. Numerical experiments demonstrate the effectiveness of our proposed algorithm.