PANOC-lite: A simpler and more efficient algorithm for composite minimization

TL;DR

PANOC-lite is a streamlined, efficient composite minimization algorithm that accelerates proximal-gradient methods with Newton-like steps, featuring a cheaper backtracking process and broader stepsize options.

Contribution

It introduces a simple linesearch method that improves efficiency and convergence for composite minimization, requiring only standard proximal-gradient oracles.

Findings

Achieves global subsequential convergence and local superlinear convergence.

Reduces computational cost by eliminating additional gradient evaluations during backtracking.

Validated on control problems and benchmark datasets, demonstrating practical effectiveness.

Abstract

This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the standard proximal-gradient oracle, similar to PANOC and ZeroFPR, provided that the nonsmooth term is convex. Noteworthy improvements include a cheaper backtracking procedure, in the sense that no additional gradients need to be evaluated, and an enlarged range of permitted stepsizes. Global subsequential convergence and local superlinear convergence are established under conventional assumptions by considering a novel merit function which is less expensive to evaluate than alternatives like the forward-backward envelope. Finally, the proposed approach is validated on model predictive control problems with collision avoidance constraints, as well as on the LIBSVM and CUTEst benchmarks.