QPALM: Proximal Augmented Lagrangian Solver for (Nonconvex) Quadratic Programs

Introduction

This is a C implementation of QPALM, a proximal augmented Lagrangian based solver for (possibly nonconvex) quadratic programs. QPALM solves problems of the form:

$$\begin{array}{rlrl}& \underset{x}{\mathrm{minimize}}& & \frac{1}{2}{x}^{\mathrm{\top }}Qx+q^{\mathrm{\top }}x\\ & \text{subject to}& & b_{\min }\le Ax\le b_{\max }\end{array}$$

Installation instructions

Python

The QPALM Python interface is available from PyPI, you can install it using:

python3 -m pip install qpalm

Julia

In the Julia console, press ] to enter the Pkg REPL and install QPALM using:

add QPALM

C/C++/Fortran

Pre-built C, C++ and Fortran libraries are available from the releases page.

Matlab

Pre-built Matlab binaries are available from the releases page. Download the version for your system and extract it into the ~/Documents/MATLAB folder.

As a one-liner in the Matlab console:

unzip('https://github.com/kul-optec/QPALM/releases/download/1.2.2/qpalm-matlab-linux.zip', userpath)

unzip('https://github.com/kul-optec/QPALM/releases/download/1.2.2/qpalm-matlab-windows.zip', userpath)

unzip('https://github.com/kul-optec/QPALM/releases/download/1.2.2/qpalm-matlab-macos.zip', userpath)

Building QPALM from source

For the full instructions to build QPALM from source, please see the Installation instructions.

Code examples

• Python interface: examples/python/qpalm_python_demo.py
• Julia interface: examples/julia/qpalm_julia_demo.jl
• C++ interface: examples/cxx/qpalm_demo.cpp
• Fortran interface: examples/fortran/qpalm_fortran_demo.f90
• C API: examples/c/qpalm_demo.c
• Matlab MEX interface: examples/matlab/qpalm_mex_demo.m and examples/matlab/qpalm_mex_nonconvex_demo.m

Citing QPALM

If you use QPALM in your research, please cite the following paper

@inproceedings{hermans2019qpalm,
    author      = {Hermans, B. and Themelis, A. and Patrinos, P.},
    booktitle   = {58th IEEE Conference on Decision and Control},
    title       = {{QPALM}: {A} {N}ewton-type {P}roximal {A}ugmented {L}agrangian {M}ethod for {Q}uadratic {P}rograms},
    year        = {2019},
    volume      = {},
    number      = {},
    pages       = {},
    doi         = {},
    issn        = {},
    month       = {Dec.},
}

License

• LGPL-3.0