#### QPPAL — a MATLAB software for high-dimensional convex quadratic programming

##### Ling Liang, Xudong Li, Defeng Sun, Kim-Chuan Toh

This software is designed to solve primal convex quadratic programming problems of the form:

\(\begin{eqnarray*}

\begin{array}{rl}

\min&\frac{1}{2}\langle x ,\, {Q}x \rangle + \langle c, \, x\rangle

\\[5pt]

{\rm s.t.}&{A}x=b

\\

& x\in \mathcal{K}

\end{array}

\end{eqnarray*}

\)

where \(Q: \mathbb{R}^n \rightarrow \mathbb{R}^n\) is a self-adjoint positive semidefinite linear operator, \(A \in \mathbb{R}^{n\times m}\) , \(c\in \mathbb{R}^n\), \(b\in \mathbb{R}^{m}\) are given data, \(\mathcal{K}\) is a simple closed convex polyhedral set defined by \(\mathcal{K}=\{x\in\mathbb{R}^n \mid \ell\leq x\leq u\}\) with \(\ell,u\in\mathbb{R}^n\) being given bounds.

Important note.

- The software is still under development. Thus it will invariably be buggy. We would appreciate your feedback and bugs’ report.
- This is a research software. It is not intended nor designed to be a general purpose software at the moment.

##### Citation

- Ling Liang, Xudong Li, Defeng Sun, and Kim-Chuan Toh, QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems,

arXiv:2103.13108.

**Copyright.** This version of QPPAL is distributed under the **3-Clause ****BSD license.**

For commercial applications that may be incompatible with this license, please contact the authors to discuss alternatives.

**Download here: QPPAL.zip**-
- unzip the package
- Run Matlab in the directory QPPAL
- After that, to see whether you have installed the software correctly, type

>> runDemo - By now, the software is ready for you to use.