# Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization

arXiv: https://arxiv.org/abs/2112.02370 · HTML: https://mlsanity.com/paper/2112.02370/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2021.

## Built on by (most cited first, 4 of 4)

- [Dual Optimistic Ascent (PI Control) is the Augmented Lagrangian Method in Disguise](https://mlsanity.com/paper/2509.22500/) (2025)
- [SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization](https://mlsanity.com/paper/2207.08195/) (2022)
- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)
- [lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layers](https://mlsanity.com/paper/2609.33630/) (2026)

## Abstract (arXiv)

This paper presents alpaqa, an open-source C++ implementation of an augmented Lagrangian method for nonconvex constrained numerical optimization, using the first-order PANOC algorithm as inner solver. The implementation is packaged as an easy-to-use library that can be used in C++ and Python. Furthermore, two improvements to the PANOC algorithm are proposed and their effectiveness is demonstrated in NMPC applications and on the CUTEst benchmarks for numerical optimization. The source code of the alpaqa library is available at https://github.com/kul-optec/alpaqa and binary packages can be installed from https://pypi.org/project/alpaqa .