論文

• James S. M. Anderson, Maho Nakata, Ryo Igarashi, Katsuki Fujisawa, Makoto Yamashita. The second-order reduced density matrix method and the two-dimensional Hubbard model, Computational and Theoretical Chemistry, Elsevier, Vol. 1003, Jan. 2013.  公式リンク  
  
• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Yoshiaki Futakata, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata. Parallel solver for SemiDefinite Programming having sparse Schur complement matrix, International Symposium on Mathematical Programming 2009, ACM Transactions on Mathematical Software, ACM, Vol. 39, No. 1, pp. 6, Nov. 2012.  公式リンク  
  
• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata. Latest developments in the SDPA Family for solving large-scale SDPs, Handbook on Semidefinite Cone and Polynomial Optimization, pp. 687-714, 2011.
• Maho Nakata, Bastiaan J. Braams, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao. Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver, The Journal of Chemical Physics, Vol. 128, No. 16, pp. 164113, Apr. 2008.
• 中田 和秀, 藤澤 克樹, 福田 光浩, 山下 真, 中田 真秀, 小林 和博. 最適化ソフトウェアSDPA, 応用数理, Vol. 18, No. 1, pp. 2--14, Mar. 2008.
• Mituhiro Fukuda, Bastiaan J. Braams, Maho Nakata, Michael L. Overton, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao. Large-scale semidefinite programs in electronic structure calculation, Mathematical Programming Series B, Vol. 109, No. 2-3, pp. 553-580, 2007.
• Maho Nakata, Bastiaan J. Braams, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao. Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions, The Journal of Chemical Physics, Vol. 125, No. 24, pp. 244109, 2006.
• Maho Nakata, Hiroshi Nakatsuji, Masahiro Ehara, Mituhiro Fukuda, Kazuhide Nakata, Katsuki Fujisawa. Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm, The Journal of Chemical Physics, Vol. 114, No. 19, pp. 8282-8292, 2001.

著書

• (M.F. Anjos, J.B. Lasserre Ed.), Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata, (M.F. Anjos, J.B. Lasserre Ed.). Latest developments in the SDPA Family for solving large-scale SDPs, Handbook on Semidefinite Cone and Polynomial Optimization, Chapter 24, Springer, 2011.
• Mituhiro Fukuda, Maho Nakata, Makoto Yamashita. Semidefinite programming: Formulations and primal-dual interior-point methods, Reduced-Density Matrix Mechanics: With Applications to Many-Electron Atoms and Molecules (D. A. Mazziotti, Ed.), John Wiley & Sons, Inc. (Hoboken), pp. 103-118, Mar. 2007.

国際会議発表 (査読有り)

• Maho Nakata, Mituhiro Fukuda, Katsuki Fujisawa. Variational approach to electronic structure calculations on second-order reduced density matrices and the N-representability problem, Workshop on the Theory of Large Coulomb System, in Complex Quantum Systems: Analysis of Large Coulomb Systems (H. Siedentop, ed.), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 24, pp. 163-194, 2013.
• Katsuki Fujisawa, Toshio Endo, Hitoshi Sato, Makoto Yamashita, Satoshi Matsuoka, Maho Nakata. High-Performance General Solver for Extremely Large-scale Semidefinite Programming Problems, International Conference for High Performance Computing, Networking, Storage and Analysis (SC12), Proceedings of IEEE/ACM International Conference for High Performance Computing, Networking, Storage and Analysis (SC12), IEEE/ACM, Nov. 2012.

国際会議発表 (査読なし・不明)

• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata. High Performance Solvers for Semidefinite Programs, KSIAM Annual Meeting 2011, Proceedings of the Korean Society for Industrial and Appplied Mathematcis, KSIAM, Vol. 6, No. 2, pp. 55-58, Nov. 2011.
• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata. Parallel Computation for SDPs Focusing on the Sparsity of Schur Complements Matrices, INFORMS Annual Meeting 2011, Nov. 2011.
• Makoto Yamashita, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata, Katsuki Fujisawa, Kazuhiro Kobayashi, Maho Nakata. SDPA: Leading-edge software for SDP, Informs Annual Meeting 2008, Oct. 2008.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata, Maho Nakata. Large-scale semidefinite programming from quantum chemistry, International Symposium on Mathematical Programming 2006, July 2006.

国内会議発表 (査読なし・不明)

• 藤澤 克樹, 小島 政和, 中田 和秀, 福田 光浩, 山下 真, 中田 真秀. SDPA project and new features of SDPA 7.1.0, 算科学の基盤技術としての高速アルゴリズムとその周辺--RIMS研究集会, 数理解析研究所講究録, Vol. 1614, pp. 136-143, Oct. 2008.

その他の論文・著書など

• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata. Parallel Computing for Large-scale Semidefinite Programs, 2010 IEEE Multi-Conference on Systems and Control, Tokyo Institute of Technology Bulletin, Vol. 29, Feb. 2013.  公式リンク  
  
• Makoto Yamashita, Katsuki Fujisawa, Kazuhide Nakata, Maho Nakata, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazushige Goto. B-460,  A high-performance software package for semidefinite programs: SDPA 7, Technical Report, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2010.
• Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Masakazu Kojima, Kazuhide Nakata, Maho Nakata, Makoto Yamashita. SDPA (SemiDefinite Programming Algorithm) User's Manual --- Version 7.0.5, Department of Mathematical and Computing Sciences Technical Report, No. 448, 2008.

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