A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives
Abstract
In this short note, we provide a simple version of an accelerated forward-backward method (a.k.a. Nesterov's accelerated proximal gradient method) possibly relying on approximate proximal operators and allowing to exploit strong convexity of the objective function. The method supports both relative and absolute errors, and its behavior is illustrated on a set of standard numerical experiments. Using the same developments, we further provide a version of the accelerated proximal hybrid extragradient method of Monteiro and Svaiter (2013) possibly exploiting strong convexity of the objective function.
Cite
@article{arxiv.2106.15536,
title = {A note on approximate accelerated forward-backward methods with absolute and relative errors, and possibly strongly convex objectives},
author = {Mathieu Barré and Adrien Taylor and Francis Bach},
journal= {arXiv preprint arXiv:2106.15536},
year = {2022}
}
Comments
Published in Open Journal on Mathematical Optimization (https://ojmo.centre-mersenne.org/item/10.5802/ojmo.12.pdf). Code available at https://github.com/mathbarre/StronglyConvexForwardBackward