Gauss-Newton meets PANOC: A fast and globally convergent algorithm for nonlinear optimal control

TL;DR

This work extends PANOC by injecting Gauss--Newton directions to accelerate convergence on nonconvex optimal control problems. By formulating the Gauss--Newton step as an equality-constrained finite-horizon LQR solvable via Riccati recursion, the approach achieves practical speedups while maintaining global convergence properties. The method leverages problem structure, including box constraints and state penalties, and introduces practical safeguards (computing GN steps every k_GN iterations) to balance cost and performance. Experimental results on a nonlinear MPC benchmark show about a twofold speedup over the L-BFGS PANOC variant, with favorable scaling as horizon length grows, and competitive real-time performance versus IPOPT.

Abstract

PANOC is an algorithm for nonconvex optimization that has recently gained popularity in real-time control applications due to its fast, global convergence. The present work proposes a variant of PANOC that makes use of Gauss-Newton directions to accelerate the method. Furthermore, we show that when applied to optimal control problems, the computation of this Gauss-Newton step can be cast as a linear quadratic regulator (LQR) problem, allowing for an efficient solution through the Riccati recursion. Finally, we demonstrate that the proposed algorithm is more than twice as fast as the traditional L-BFGS variant of PANOC when applied to an optimal control benchmark problem, and that the performance scales favorably with increasing horizon length.

Figures (8)

• Figure 1: PANOC$^+$de_marchi_proximal_2022 with Gauss--Newton acceleration
• Figure 2: Forward simulation
• Figure 3: Backward gradient evaluation
• Figure 4: LQR factor
• Figure 5: LQR solve