QPDO: the Quadratic Primal-Dual Optimizer

QPDO is a numerical solver for optimization problems in the form

minimize        0.5 x' Q x + q' x

subject to      l <= A x <= u

where x in R^n is the decision variable. The symmetric positive semidefinite matrix Q in S_+^n, the vector q in R^n, and the matrix A in R^{m x n} are bounded. The vectors l in R^m U {-inf}^m and u in R^m U {+inf}^m are extended-real-valued and satisfy l_i ⩽ u_i for all i in 1,...,m.

Method and Citing

QPDO implements a primal-dual Newton proximal method for convex quadratic programming. Details can be found in the research paper, currently under review. The preprint is freely available here, and serves as a user manual for advanced users. If you use QPDO in your work, we kindly ask that you cite the following reference.

@article{qpdo,
	author      = {De~Marchi, Alberto},
	title       = {On a Primal-Dual Newton Proximal Method for Convex Quadratic Programs},
	journal     = {Preprint},
	year        = {2020},
	month       = {12},
	doi         = {10.13140/RG.2.2.33215.12964},
	note        = {Submitted},
}

Installation

QPDO is implemented in C and provides a MATLAB interface via mex.

Clone this repository with the submodule for SuiteSparse, running

git clone https://github.com/aldma/qpdo.git
cd qpdo
git submodule update --init --recursive

Matlab

• To install the mex interface of QPDO, add QPDO and its subfolders to the MATLAB path. Then go to interfaces/mex/ and run qpdo_make.m. You can test and see how to call QPDO from MATLAB using demo_mex.m in the examples/ folder.

Benchmarks

We are currently benchmarking QPDO against OSQP and QPALM, looking forward to sharing the results.

Get in touch

Although this software package is still in its infancy, don't hesitate to share your impression! Would you like to collaborate to build better software? Here we are!