Petascale general solver for semidefinite programming problems with over two million constraints

Katsuki Fujisawa, Toshio Endo, Yuichiro Yasui, Hitoshi Sato, Naoki Matsuzawa, Satoshi Matsuoka, Hayato Waki

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    10 Citations (Scopus)

    Abstract

    The semi definite programming (SDP) problem is one of the central problems in mathematical optimization. The primal-dual interior-point method (PDIPM) is one of the most powerful algorithms for solving SDP problems, and many research groups have employed it for developing software packages. However, two well-known major bottlenecks, i.e., the generation of the Schur complement matrix (SCM) and its Cholesky factorization, exist in the algorithmic framework of the PDIPM. We have developed a new version of the semi definite programming algorithm parallel version (SDPARA), which is a parallel implementation on multiple CPUs and GPUs for solving extremely large-scale SDP problems with over a million constraints. SDPARA can automatically extract the unique characteristics from an SDP problem and identify the bottleneck. When the generation of the SCM becomes a bottleneck, SDPARA can attain high scalability using a large quantity of CPU cores and some processor affinity and memory interleaving techniques. SDPARA can also perform parallel Cholesky factorization using thousands of GPUs and techniques for overlapping computation and communication if an SDP problem has over two million constraints and Cholesky factorization constitutes a bottleneck. We demonstrate that SDPARA is a high-performance general solver for SDPs in various application fields through numerical experiments conducted on the TSUBAME 2.5 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 1.713 PFlops in double precision for large-scale Cholesky factorization using 2,720 CPUs and 4,080 GPUs.

    Original languageEnglish
    Title of host publicationProceedings - IEEE 28th International Parallel and Distributed Processing Symposium, IPDPS 2014
    PublisherIEEE Computer Society
    Pages1171-1180
    Number of pages10
    ISBN (Print)9780769552071
    DOIs
    Publication statusPublished - Jan 1 2014
    Event28th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2014 - Phoenix, AZ, United States
    Duration: May 19 2014May 23 2014

    Publication series

    NameProceedings of the International Parallel and Distributed Processing Symposium, IPDPS
    ISSN (Print)1530-2075
    ISSN (Electronic)2332-1237

    Other

    Other28th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2014
    CountryUnited States
    CityPhoenix, AZ
    Period5/19/145/23/14

    All Science Journal Classification (ASJC) codes

    • Computational Theory and Mathematics
    • Computer Networks and Communications
    • Hardware and Architecture
    • Software

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