Kazuhide Nakata

A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix Completion

  • Katsuki Fujisawa
  • Masakazu Kojima
  • Kazuhide Nakata
  • Makoto Yamashita
    • Categories Graphs and Matroids, Parallel Algorithms, Semi-definite Programming Tags , , , , ,

    A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of … Read more

    Exploiting Sparsity in Semidefinite Programming via Matrix Completion II: Implementation and Numerical Results

  • Katsuki Fujisawa
  • Mituhiro Fukuda
  • Masakazu Kojima
  • Kazuo Murota
  • Kazuhide Nakata
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    In Part I of this series of articles, we introduced a general framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefinite programs (SDPs) when solving them by primal-dual interior-point methods. This framework is based on some results about positive semidefinite matrix completion, and it can be embodied … Read more