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:

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

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

For more information, please see Getting started.