Efficient Parallel Implementation for Extremely Large-Scale SemiDefinite Programming

2008 Fiscal Year Final Research Report

• Project/Area Number: 18710141
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Social systems engineering/Safety system
• Research Institution: Tokyo Institute of Technology (2008); Kanagawa University (2006-2007)
• Principal Investigator: YAMASHITA Makoto Tokyo Institute of Technology, 大学院・情報理工学研究科, 助教 (20386824)
• Project Period (FY): 2006 – 2008
• Keywords: 数理計画法 / 並列計算 / 半正定値計画問題

Research Abstract

半正定値計画問題は、量子化学や制御理論など幅広い応用を持つ重要な数理計画問題である。しかしながら、量子化学などから発生する半正定値計画問題は大規模になる傾向が強く、一台の計算機では求解が難しい。本研究では、Schur補完行列にかかる計算に並列計算を適用することで、既存ソフトウェアでは不可能であった大規模な半正定値計画問題の求解を実現した。さらに行列の特徴を活用し、高い並列効果を得ることに成功した。

Research Products

• [Journal Article] Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver (2008)
  • Author(s): Maho Nakata, Bastiaan Braams, Katsuki Fujisawa, Mituhiro Fukuda, Jerome Percus, Makoto Yamashita and Zhengji Zhao
  • Journal Title: Journal of Chemical Physics Vol. 128 Pages: 164113
  • Peer Reviewed
• [Journal Article] 最適化ソフトウェアSDPA (2008)
  • Author(s): 中田和秀、藤澤克樹、福田光浩、山下真、 中田真秀、小林和博
  • Journal Title: 応用数理 Vol. 18, No. 1 Pages: 2-14
  • Peer Reviewed
• [Journal Article] Parallel Solver for SemiDefinite Programming (2007)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa and Kazuhide Nakata
  • Journal Title: International Journal of Logistics and SCM systems Vol. 2, No. 1 Pages: 22-29
  • Peer Reviewed
• [Journal Article] SDPA Project: Solving Large-Scale Semidefinite Programs (2007)
  • Author(s): Katsuki Fujisawa, Kazuhide Nakata, Makoto Yamashita and Mituhiro Fukuda
  • Journal Title: Journal of the Operations Research Society of Japan Vol. 50, No. 4 Pages: 278-298
  • Peer Reviewed
• [Journal Article] Large-scale semidefinite programs in electronic structure calculation (2007)
  • Author(s): Mituhiro Fukuda, Bastiaan Braams, Maho Nakata, Michael Overton, Jerome Percus, Makoto Yamashita and Zhengji Zhao
  • Journal Title: Mathematical Programming B Vol. 109, No. 2 Pages: 553-580
  • Peer Reviewed
• [Journal Article] 量子化学における超大規模半正定値計画問題と並列計算による高速求解(招待講演) (2006)
  • Author(s): 山下真
  • Journal Title: 第18回RAMPシンポジウム論文集 Pages: 191-207
• [Journal Article] Solving Large Scale Optimization Problems via Grid and Cluster Computing (2006)
  • Author(s): Katsuki Fujisawa, Masakazu Kojima, Akiko Takeda and Makoto Yamashita
  • Journal Title: Journal of the Operation Research Society of Japan Vol. 47, No. 4 Pages: 265-274
  • Peer Reviewed
• [Journal Article] Simple Hamiltonians which exhibit drastic failures by variational determination (2006)
  • Author(s): Maho Nakata, Bastiaan Braams, Mituhiro Fukuda, Jerome Percus, Makoto Yamashita and Zhengji Zhao
  • Journal Title: Journal of Chemical Physics Vol. 125 Pages: 244109
  • Peer Reviewed
• [Journal Article] A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs (2006)
  • Author(s): Kazuhide Nakata, Makoto Yamashita, Katsuki Fujisawa and Masakazu Kojima
  • Journal Title: Parallel Computing Vol. 32, No. 1 Pages: 24-43
  • Peer Reviewed
• [Presentation] SDPA : Leading-edge Software for SDP (2008)
  • Author(s): Makoto Yamashita
  • Organizer: INFORMS Annual Meeting 2008
  • Place of Presentation: Washington DC
  • Year and Date: 2008-10-14
• [Presentation] Computational Time Estimation for SDP solvers (2007)
  • Author(s): Makoto Yamashita
  • Organizer: INFORMS Annual Meeting 2007
  • Place of Presentation: Seattle
  • Year and Date: 2007-11-14
• [Presentation] Parallel Solver for SemiDefinite Programming (2007)
  • Author(s): Makoto Yamashita
  • Organizer: The Third International Conference of Logistics and SCM
  • Place of Presentation: 横浜
  • Year and Date: 2007-08-30
• [Presentation] 量子化学における 超大規模半正定値計画問題と並列計算による高速求解 (2006)
  • Author(s): 山下真
  • Organizer: 第18回RAMPシンポジウム
  • Place of Presentation: 京都
  • Year and Date: 2006-10-13
• [Presentation] Large-scale semidefinite programming from quantum chemistry (2006)
  • Author(s): Makoto Yamashita
  • Organizer: International Symposium on Mathematical Programming 2006
  • Place of Presentation: Rio de Janeiro
  • Year and Date: 2006-07-31
• [Book] Reduced-Density-Matrix Mechanics with Applications to Many-Electron Atoms and Moecules (2007)
  • Author(s): Mituhiro Fukuda, Maho Nakata and Makoto Yamashita
  • Total Pages: 574
  • Publisher: John Wiley & Sons, Inc. (pp. 103-118)
• [Book] Parallel Combinatorial Optimization (2006)
  • Author(s): Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima and Kazuhide Nakata
  • Total Pages: 330
  • Publisher: Wiley-Interscience (pp. 211-238)
• [Remarks] 半正定値計画問題ソフトウェアSDPAおよびその並列版SDPARAのホームページ
  • URL: http://sdpa.indsys.chuo-u.ac.jp/sdpa/
• [Remarks] 論文の研究成果は東京工業大学のレポジトリT2R2でも公開している。
  • URL: http://t2r2.star.titech.ac.jp/