  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.
