In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and the ScaLAPACK library. A new feature is implemented to deal with problems that have rank-one constraint matrices. We show that significant improvement is obtained for a test set of problems with rank one constraint matrices. Moreover, we show that very good parallel efficiency is obtained for large-scale problems where the number of linear equality constraints is very large compared to the block sizes of the positive semidefinite matrix variables.
Citation
Ivanov, I.D., & Klerk, E. de (2007). Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster. (CentER Discussion Paper, 2007-20) pp. 1-22. Revised on February 6th, 2008.