# Proximal gradient methods beyond monotony

arXiv: https://arxiv.org/abs/2211.04827 · HTML: https://mlsanity.com/paper/2211.04827/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization](https://mlsanity.com/paper/2409.19428/) (2024)

## Abstract (arXiv)

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal gradient methods, which often rely on a line search procedure as globalization mechanism. We consider an adaptive nonmonotone proximal gradient scheme based on an averaged merit function and establish asymptotic convergence guarantees under weak assumptions, delivering results on par with the monotone strategy. Global worst-case rates for the iterates and a stationarity measure are also derived. Finally, a numerical example indicates the potential of nonmonotonicity and spectral approximations.