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

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

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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.

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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.

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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.

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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.

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• 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.