alpaqa 1.0.0a14

Augmented Lagrangian and PANOC solvers for nonconvex numerical optimization.

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.

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

\begin{equation*} \begin{aligned} & \underset{x}{\textbf{minimize}} & & f(x) &&&& f : {{\rm I\mathchoice{\hspace{-2pt}}{\hspace{-2pt}}{\hspace{-1.75pt}}{\hspace{-1.7pt}}R}}^n \rightarrow {{\rm I\mathchoice{\hspace{-2pt}}{\hspace{-2pt}}{\hspace{-1.75pt}}{\hspace{-1.7pt}}R}} \\ & \textbf{subject to} & & \underline{x} \le x \le \overline{x} \\ &&& \underline{z} \le g(x) \le \overline{z} &&&& g : {{\rm I\mathchoice{\hspace{-2pt}}{\hspace{-2pt}}{\hspace{-1.75pt}}{\hspace{-1.7pt}}R}}^n \rightarrow {{\rm I\mathchoice{\hspace{-2pt}}{\hspace{-2pt}}{\hspace{-1.75pt}}{\hspace{-1.7pt}}R}}^m \end{aligned} \end{equation*}

Documentation

• Sphinx documentation

• Python examples

• Doxygen documentation

• C++ examples

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

• P. Pas, M. Schuurmans, and P. Patrinos, “Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization,” 20th European Control Conference (ECC), Jul. 2022 (arXiv)