Abstract: The SDPA (SemiDefinite Programming Algorithm) is known as efficient computer software based on primal-dual interior-point method for solving SDPs (Semidefinite Programs). In many applications, however, some SDPs become larger and larger, too large for the SDPA to solve on a single processor. In execution of the SDPA applied to large scale SDPs, the computation of the so-called Schur complement matrix and its Cholesky factorization consume most of the computational time. The SDPARA (SemiDefinite Programming Algorithm PARAllel version) is a parallel version of the SDPA on multiple processors and distributed memory, which replaces these two parts by their parallel implementation using MPI and ScaLAPACK. Through numerical results, we show that the SDPARA on a PC cluster consisting of 64 processors attains high scalability for large scale SDPs without losing the stability of the SDPA.
Parallel Computing Vol.29 (8) 1053-1067 (2003).