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

Abstract

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.

References in corpus (2)

• Embedded nonlinear model predictive control for obstacle avoidance using PANOC
• Constrained composite optimization and augmented Lagrangian methods

Cited by in corpus (9)

• Constrained composite optimization and augmented Lagrangian methods
• Proximal gradient methods beyond monotony
• Implicit augmented Lagrangian and generalized optimization
• Local properties and augmented Lagrangians in fully nonconvex composite optimization
• Gauss-Newton meets PANOC: A fast and globally convergent algorithm for nonlinear optimal control
• PANTR: A proximal algorithm with trust-region updates for nonconvex constrained optimization
• An interior proximal gradient method for nonconvex optimization
• SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization
• Proximal Dogleg Opportunistic Majorization for Nonconvex and Nonsmooth Optimization