alpaqa

alpaqa is an efficient implementation of an augmented Lagrangian method for general nonlinear programming problems, which uses the first-order, matrix-free PANOC algorithm as an inner solver.
The numerical algorithms themselves are implemented in C++ for optimal performance, and they are exposed as an easy-to-use Python package. An experimental MATLAB interface is available as well.

The solvers in this library solve minimization problems of the following form:

$$\begin{array}{rlrlrlrl}& \underset{x}{\mathbf{\text{minimize}}}& & f(x)& & & & f:{\mathrm{I}\mathrm{R}}^n\to \mathrm{I}\mathrm{R}\\ & \mathbf{\text{subject to}}& & \underset{―}{x}\le x\le \bar{x}\\ & & & \underset{―}{z}\le g(x)\le \bar{z}& & & & g:{\mathrm{I}\mathrm{R}}^n\to {\mathrm{I}\mathrm{R}}^m\end{array}$$

Documentation

• Documentation (Sphinx)
• Python examples
• C++ documentation (Doxygen)
• C++ examples
• Matlab documentation

Installation

The Python interface can be installed directly from PyPI:

python3 -m pip install --upgrade --pre alpaqa

For more information, please see the full installation instructions.

Publications

Pieter Pas, Mathijs Schuurmans, and Panagiotis Patrinos. Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization. In 2022 European Control Conference (ECC), pages 417–422, 2022.