Makoto Yamashita

SFSDP: a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems

  • Sunyoung Kim
  • Masakazu Kojima
  • Hayato Waki
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , ,

    SFSDP is a Matlab package for solving a sensor network localization problem. These types of problems arise in monitoring and controlling applications using wireless sensor networks. SFSDP implements the semidefinite programming (SDP) relaxation proposed in Kim et al. [2009] for sensor network localization problems, as a sparse version of the full semidefinite programming relaxation (FSDP) … Read more

    User’s Manual for SparseCoLO: Conversion Methods for Sparse Conic-form Linear Optimization Problems

  • Katsuki Fujisawa
  • Sunyoung Kim
  • Masakazu Kojima
  • Y. Okamoto
  • Makoto Yamashita
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , ,

    SparseCoLO is a Matlab package for implementing the four conversion methods, proposed by Kim, Kojima, Mevissen, and Yamashita, via positive semidefinite matrix completion for an optimization problem with matrix inequalities satisfying a sparse chordal graph structure. It is based on quite a general description of optimization problem including both primal and dual form of linear, … Read more

    Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion

  • Sunyoung Kim
  • Masakazu Kojima
  • Martin Mevissen
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , ,

    A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two … Read more

    Parallel Primal-Dual Interior-Point Methods for SemiDefinite Programs

  • Katsuki Fujisawa
  • Mituhiro Fukuda
  • Masakazu Kojima
  • Kazuhide Nakata
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , ,

    The Semidefinite Program (SDP) is a fundamental problem in mathematical programming. It covers a wide range of applications, such as combinatorial optimization, control theory, polynomial optimization, and quantum chemistry. Solving extremely large-scale SDPs which could not be solved before is a significant work to open up a new vista of future applications of SDPs. Our … Read more

    Large-scale semidefinite programs in electronic structure calculation

  • Bastiaan J. Braams
  • Mituhiro Fukuda
  • Michael L. Overton
  • Maho Nakata
  • Jerome K. Percus
  • Makoto Yamashita
  • Zhengji Zhao
    • Categories Basic Sciences Applications, Semi-definite Programming Tags , , , , ,

    Employing the variational approach having the two-body reduced density matrix (RDM) as variables to compute the ground state energies of atomic-molecular systems has been a long time dream in electronic structure theory in chemical physics/physical chemistry. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual … Read more

    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

    SDPARA : SemiDefinite Programming Algorithm PARAllel Version

  • Katsuki Fujisawa
  • Masakazu Kojima
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , , , ,

    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 … Read more

    Implementation and Evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0

  • Katsuki Fujisawa
  • Masakazu Kojima
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , , , ,

    The SDPA (SemiDefinite Programming Algorithm) is a software package for solving general SDPs(SemiDefinite Programs). It is written in C++ with the help of {\it LAPACK} for numerical linear algebra for dense matrix computation. The purpose of this paper is to present a brief description of the latest version of the SDPA and its high performance … Read more