# Proximal Gradient Algorithms under Local Lipschitz Gradient Continuity: A Convergence and Robustness Analysis of PANOC

arXiv: https://arxiv.org/abs/2112.13000 · HTML: https://mlsanity.com/paper/2112.13000/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2021.

## Built on by (most cited first, 4 of 4)

- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [Adversarial Attacks and Defenses in Machine Learning-Powered Networks: A Contemporary Survey](https://mlsanity.com/paper/2303.06302/) (2023)
- [On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithms](https://mlsanity.com/paper/2311.18431/) (2023)
- [SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization](https://mlsanity.com/paper/2207.08195/) (2022)

## Abstract (arXiv)

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local Lipschitz gradient continuity for the smooth part of the objective function. We investigate an adaptive scheme for PANOC-type methods (Stella et al. in Proceedings of the IEEE 56th CDC, 1939--1944, 2017), namely accelerated linesearch algorithms requiring only the simple oracle of proximal gradient. While including the classical proximal gradient method, our theoretical results cover a broader class of algorithms and provide convergence guarantees for accelerated methods with possibly inexact computation of the proximal mapping. These findings have also significant practical impact, as they widen scope and performance of existing, and possibly future, general purpose optimization software that invoke PANOC as inner solver.