SDPNAL version 0, -- a MATLAB software for semidefinite programming based on a semi-smooth Newton-CG augmented Lagrangian method

Xinyuan Zhao, Defeng Sun, and Kim-Chuan Toh

The software is designed to solve standard primal and dual SDPs of the form: 
   min{(C1,X1) + ... + (CN,XN): A1(X1) + ... + AN(XN) = b, X1,...,XN psd}

   max{(b,y) : A1t(y) + Z1 = C1,...,ANt(y) + ZN = CN, Z1,..,ZN psd}

   where Xk, Zk are either symmetric positive definite matrices or non-negative vectors.
Important note: 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 accurately.
This software package is designed for solving standard SDP problems with max{n1,...,nN} (nk=dimension of matrix variable Xk) up to 2000. The number of linear equality constraints (dimension of b) can be large. In our numerical experiments, we have successfully solved SDPs with m > 1 million.
For more details, see:
  • Xinyuan Zhao, Defeng Sun, and Kim-Chuan Toh, A Newton-CG Augmented Lagrangian Method for Semidefinite Programming, SIAM J. Optimization, to appear.