Proximal Gradient Algorithms Under Local Lipschitz Gradient Continuity

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