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.
QPDO implements a primal-dual Newton proximal method for convex quadratic programming. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. In particular, all linear systems are solvable by construction, independently from the problem data, and an exact linesearch can be performed. Details can be found in the research paper mentioned below, which 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{demarchi2022qpdo,
author = {De~Marchi, Alberto},
title = {On a primal-dual {N}ewton proximal method for convex quadratic programs},
journal = {Computational Optimization and Applications},
year = {2022},
volume = {81},
number = {2},
pages = {369--395},
doi = {10.1007/s10589-021-00342-y},
}
QPDO is implemented in C and provides a MATLAB interface via mex, inspired by OSQP and QPALM.
Clone this repository with the submodule for SuiteSparse, running
git clone https://github.com/aldma/qpdo.git
cd qpdo
git submodule update --init --recursive
- 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 usingdemo_mex.min the examples/ folder.
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