# QPPAL

#### 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.