The International Conference for High Performance Computing, Networking, Storage and Analysis
Peta-Scale General Solver for Semidefinite Programming Problems with Over Two Million Constraints.
Authors: Katsuki Fujisawa (Chuo University and JST CREST), Toshio Endo (Tokyo Institute of Technology and JST CREST), Hitoshi Sato (Tokyo Institute of Technology and JST CREST), Yuichiro Yasui (Chuo University and JST CREST), Naoki Matsuzawa (Tokyo Institute of Technology), Hayato Waki (Kyushu University)
Abstract: SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical optimization. We have developed the new version of SDPARA, which is a parallel implementation on multiples CPUs and GPUs for solving large-scale SDP problems. SDPARA can attain high scalability using a large number of CPU cores and some techniques of processor affinity and memory interleaving. SDPARA can also perform the parallel Cholesky factorization using thousands of GPUs and techniques to overlap the computation and communication if an SDP problem has over a million constraints. We demonstrate that SDPARA is a peta-scale general solver for SDP problems in various application fields through numerical experiments on the TSUBAME 2.0 supercomputer and we solved the largest SDP problem (which has over 2.33 million constraints), thereby creating a new world record. Our implementation also achieved 1.018 PFlops in double precision for large-scale Cholesky factorization using 2,720 CPUs and 4,080 GPUs.