ProxNLP: a primal-dual augmented Lagrangian solver for nonlinear programming in Robotics and beyond

TL;DR

ProxNLP introduces a primal-dual augmented Lagrangian solver tailored for nonlinear constrained optimization on manifolds, enhancing robustness and speed for robotics and control applications.

Contribution

It presents a novel primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, with an efficient C++ implementation for robotics.

Findings

Effective handling of inequality constraints on manifolds.

Robust and fast optimization suitable for robotics applications.

Open-source C++ implementation available.

Abstract

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie groups), along with a specific requirement for robustness and speed. In recent years, augmented Lagrangian methods have seen a resurgence due to their robustness and flexibility, their connections to (inexact) proximal-point methods, and their interoperability with Newton or semismooth Newton methods. In the sequel, we present primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, which we introduced in our recent work, as well as an efficient C++ implementation suitable for use in robotics applications and beyond.