The scalable petascale data-driven approach for the Cholesky factorization with multiple GPUs

The Cholesky factorization is an important linear algebra kernel which is used in the semidefinite programming (SDP) problem. However, the large computation costs for Cholesky factorization of the Schur complement matrix (SCM) has been obstacles to solve large scale problems. This paper describes a brand-new version of the parallel SDP solver, SDPARA, which has been equipped with a Cholesky factorization implementation and demonstrated 1.7PFlops performance with over two million constraints by using 4,080 GPUs. The performance and scalability is even more improved by introducing a data-driven approach, rather than traditional synchronous approach. Also we point out that typical data-driven implementations have limitation in scalability, and demonstrate the efficiency of the proposed approach via experiments on TSUBAME2.5 supercomputer.