# SDPNALplus

#### SDPNALplus version 1.0 — a MATLAB software for semidefinite programming with bound constraints

Defeng Sun, Kim-Chuan Toh
Corresponding author: Kim-Chuan Toh

Past contributors: Xinyuan Zhao (for SDPNAL), Liuqin Yang (for SDPNALplus  published in MPC), Yancheng Yuan (for a basic user friendly interface)

This software is designed to solve primal SDP of the form:

$$\begin{eqnarray*} \begin{array}{rl} \min&\langle C_1,X_1\rangle+\cdots+\langle C_N,X_N\rangle \\[5pt] {\rm s.t.}&{\cal A}_1(X_1)+\cdots+{\cal A}_N(X_N)=b \\[5pt] &l\leq{\cal B}_1(X_1)+\cdots+{\cal B}_N(X_N)\leq u \\[5pt] & X_k\succeq 0,\;L_k\leq X_k\leq U_k,\quad k=1,\ldots,N \end{array} \end{eqnarray*}$$

where $$$X_k$$$ are either symmetric matrices or column vectors. Linear inequality constraints are also allowed; for details, see the users’ guide in the package.

Important note.

• The software is still under development. Thus it will invariably be buggy. We would appreciate your feedback and bugs’ report to the corresponding author: Kim-Chuan Toh (mattohkc@nus.edu.sg).
• This is a research software. It is not intended nor designed to be a general purpose software at the moment. The solver is expected to be robust if the primal and dual SDPs are both non-degenerate at the optimal solutions. However, if either of one of them is degenerate, then the solver may not be able to solve the SDPs to high accuracy.
• This software package is designed for solving SDP problems with (=dimension of matrix variable ) up to 5000. The number of linear equality constraints ( = dimension of ) can be large. In our numerical experiments, we have successfully solved SDPs with millions.
• Detailed computational results (computed in Dec 2017) for over 500 problems tested in the following papers.

##### Citation
• L.Q. Yang, D.F. Sun, and K.C. Toh, SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints, Mathemtical Programming Computation, 7 (2015), pp. 331-366. arXiv:1406.0942.
• Xinyuan Zhao, Defeng Sun, and Kim-Chuan Toh, A Newton-CG Augmented Lagrangian Method for Semidefinite Programming, SIAM J. Optimization, 20 (2010), pp. 1737–1765.