Implementation Issues in CSDP

CSDP is a software package that implements the XZ primal–dual interior point method for semidefinite programming. In this method there are a number of computationally intensive steps including the construction of the Schur complement matrix O, the factorization of O, multiplications and Cholesky factorizations of matrices of size n. Profiling shows that for different problems, each of these types of operations can dominate the CPU time used by CSDP. We discuss ways in which the performance of these operations has been optimized in CSDP. We also discuss techniques for improving the accuracy of the solutions by scaling and ignoring small pivots in the factorization of the Schur complement matrix. As with interior point methods for linear programming, we have found that this can improve the accuracy of the solutions that are obtained.