Alpaqa

Alpaqa is an efficient implementation of the 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:

\[\begin{split}\newcommand\mymathbb[1] { {\rm I\mathchoice{\hspace{-2pt}}{\hspace{-2pt}} {\hspace{-1.75pt}}{\hspace{-1.7pt}}#1} } \newcommand{\Re}{\mymathbb R} \begin{aligned} & \underset{x}{\text{minimize}} & & f(x) &&&& f : \Re^n \rightarrow \Re \\ & \text{subject to} & & \underline{x} \le \phantom{g(}x\phantom{)} \le \overline{x} \\ &&& \underline{z} \le g(x) \le \overline{z} &&&& g : \Re^n \rightarrow \Re^m \end{aligned}\end{split}\]

The objective function \(f(x)\) and the constraints function \(g(x)\) should have a Lipschitz-continuous gradient.

For more information, please see Getting started.