QPALM

Platform	CI Status
Linux
OSX

A proximal augmented Lagrangian method for (possibly nonconvex) QPs using semismooth Newton direction and exact line search.

Installation

Matlab

• To install the mex interface of QPALM, add QPALM and its subfolders to the matlab path. Then run qpalm_make.m. You can test whether QPALM is working using the examples/qpalm_mex_demo.m and examples/qpalm_mex_nonconvex_demo.m.

C

• To install a C-callable library, check Bintray for the binaries. These were compiled against intel mkl and lapack from conda. So install miniconda and run the following commands

conda install -c conda-forge lapack
conda install -c intel mkl
export LD_LIBRARY_PATH=path-to-miniconda/lib/:$LD_LIBRARY_PATH
export LD_LIBRARY_PATH=path-to-qpalm-binaries/lib/:$LD_LIBRARY_PATH

Python

The python interface has been compiled for python version 3.7. If you want to use a different version, do your own install with the instructions on custom compilation below.

Follow the instructions for installing the C-library above. Then in an open terminal, do

export LD_LIBRARY_PATH=path-to-qpalm-binaries/interfaces/python/build/lib/:$LD_LIBRARY_PATH
python3 path-to-qpalm-binaries/interfaces/python/qpalm_python_demo.py

Julia

See QPALM.jl for the instructions on installing the Julia interface.

Custom Compilation

If you wish to do a custom compilation of the shared libraries, take a look at buildCustom.sh. First install the dependencies

conda install -c conda-forge lapack
conda install -c intel mkl

Then change the following lines near the top of the script

export MINICONDA_LIB=path-to-miniconda/lib
export MINICONDA_INCLUDE=path-to-miniconda/include

Furthermore, change the cmake line to have whatever flags you want. To build the release version (with tests), use

cmake $curdir -DCMAKE_BUILD_TYPE=release -DCOVERAGE=ON

To build the python interface, use instead

cmake path-to-QPALM -DCMAKE_BUILD_TYPE=release -DINTERFACES=OFF -DUNITTESTS=OFF -DPYTHON=ON

Finally, run the buildCustom.sh script

chmod 755 buildCustom.sh
./buildCustom.sh

Code Examples

Basic demos are available for the different ways to call the solver:

• For the mex interface of QPALM, check out examples/qpalm_mex_demo.m and examples/qpalm_mex_nonconvex_demo.m.

• For the C-version of QPALM, check out examples/qpalm_demo.c.

• For the python interface of QPALM, check out interfaces/python/qpalm_python_demo.py.

• For the Julia interface of QPALM, check out any of the files in interfaces/QPALM.jl/test/.

Documentation

You can now find the the documentation online.

Tests

The QPALM library is tested extensively. The tests currently have . To build the debug version and run the automated tests yourself, check out the custom compilation section above.

Benchmarks (random QPs)

Contributors

• Ben Hermans - Main developer

• Panagiotis Patrinos - Codeveloper

• Andreas Themelis - Theoretical contributions

Citing

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

QPALM is licensed under GPL v3.0. Some modules are used in this software:

• Suitesparse: authored by Tim Davis. Each of its modules is licensed separately, see suitesparse/LICENSE.txt. The main module used in QPALM is CHOLMOD.

• Intel MKL: authored by the Intel Corporation and licensed under the Intel Simplified Software License.

• LOBPCG: the version of LOBPCG used here was written by Ben Hermans and licensed under the GNU Lesser General Public License v3.0, see LOBPCG/LICENSE.

• LAPACK: authored by The University of Tennessee and The University of Tennessee Research Foundation, The University of California Berkeley, and The University of Colorado Denver, and licensed under BSD-3, see here.

• Minunit: a minimal unit testing framework for C, originally authored by David Siñuela Pastor and licensed under MIT, see here.