PANTR: A proximal algorithm with trust-region updates for nonconvex constrained optimization

TL;DR

PANTR is a novel solver for nonconvex constrained optimization that combines trust-region updates with forward-backward iterations, leveraging Hessian information for fast and reliable solutions, especially in control applications.

Contribution

The paper introduces PANTR, a new proximal algorithm with trust-region updates that efficiently solves nonconvex constrained problems by exploiting Hessian information and structure.

Findings

Effective in nonlinear model predictive control

Exploits Hessian information for faster convergence

Open-source implementation available

Abstract

This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with solutions to trust-region subproblems: the former ensures global convergence, whereas the latter enables fast update directions. We discuss how the algorithm is able to exploit exact Hessian information of the smooth objective term through a linear Newton approximation, while benefiting from the structure of box-constraints or l1-regularization. An open-source C++ implementation of PANTR is made available as part of the NLP solver library ALPAQA. Finally, the effectiveness of the proposed method is demonstrated in nonlinear model predictive control applications.