# QSDPNAL

### QSDPNAL version 1.0 — a MATLAB software for convex quadratic semidefinite programming

Xudong Li, Defeng Sun, Kim-Chuan Toh

This software is designed to solve convex quadratic SDP of the form:

$\min \left\{\frac{1}{2}\langle X, {\cal Q} X \rangle + \langle C, X \rangle \mid {\cal A} X= b, \; X\in {\cal S}_+^n \cap {\cal K} \right\},$ where ${\cal Q}:{\cal S}_n\to {\cal S}_n$ is a self-adjoint positive semidefinite linear operator, ${\cal A}:{\cal S}_n \rightarrow \mathbb{R}^{m}$ is a linear map, $C\in {\cal S}_n$, $b \in \mathbb{R}^{m}$ are given data, ${\cal K}$ is a simple nonempty closed convex polyhedral set in ${\cal S}_n$, such as ${\cal K} =\{X \in{\cal S}_n \mid\, L\leq X\leq U\}$ with $L,U\in {\cal S}_n$ being given matrices.

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:

• Xudong Li, Defeng Sun, and Kim-Chuan Toh, QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming, Mathematical Programming Computation, 10 (2018), pp. 703–743.