論文

• Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Exact SDP relaxations for quadratic programs with bipartite graph structures, Journal of Global Optimization, Dec. 2022.
• Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Exact SDP relaxations of quadratically constrained quadratic programs with forest structures, Journal of Global Optimization, Vol. 82, pp. 243-262, Feb. 2022.
• Takashi Nakagaki, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. A dual spectral projected gradient method for log-determinant semidefinite problems, Computational Optimization and Applications, Vol. 76, No. 1, pp. 33-68, May 2020.
• 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.
• Katsuki Fujisawa, Kazuhide Nakata, Makoto Yamashita, Mituhiro Fukuda. SDPA Project : Solving Large-scale Semidefinite Programs, Journal of the Operations Research Society of Japan, Vol. 50, No. 4, pp. 278-298, 2007.
• 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.
• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Parallel primal-dual interior-point methods for semidefinite programs, Parallel Combinatorial Optimization (El-G. Talbi, Ed.), John Wiley & Sons, Inc. (Hoboken), Vol. 32, No. 1, pp. 211-238, Oct. 2006.
• Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata. Preprocessing sparse semidefinite programs via matrix completion, Optimization Methods and Software, Vol. 21, No. 1, pp. 17-39, 2006.
• 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.
• Zhengji Zhao, Bastiaan J. Braams, Mituhiro Fukuda, Michael L. Overton, Jerome K. Percus. The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions, The Journal of Chemical Physics, Vol. 120, No. 5, pp. 2095-2104, 2004.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota. Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results, Mathematical Programming, Vol. Series B 95, No. 2, pp. 303-327, 2003.
• Mituhiro Fukuda, Masakazu Kojima, Masayuki Shida. Lagrangian dual interior-point methods for semidefinite programs, SIAM Journal on Optimization, Vol. 12, No. 4, pp. 1007-1031, 2002.
• 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.
• Mituhiro Fukuda, Masakazu Kojima. Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem, Computational Optimization and Applications, Vol. 19, No. 1, pp. 79-105, 2001.
• Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota, Kazuhide Nakata. Exploiting sparsity in semidefinite programming via matrix completion I: General framework, SIAM Journal on Optimization, Vol. 11, No. 3, pp. 647-674, 2000.

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.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel primal-dual interior-point methods for semidefinite programs, Parallel Combinatorial Optimization (El-G. Talbi, Ed.), Chapter 9, John Wiley ＆ Sons, Inc, 2006.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Numerical evaluation of the SDPA (semidefinite programming algorithm), High Performance Optimization (Frenk, H., Roos, K., Terlaky, T., Zhang, S. Eds.), Chapter 11, Springer, 2000.

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.
• Akiko Takeda, Yang Dai, Mituhiro Fukuda, Masakazu Kojima. Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems (P. M. Pardalos, Ed.), Kluwer Academic Publishers (Dorchecht), pp. 489-510, 2000.

国際会議発表 (査読なし・不明)

• Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita*. Tightness conditions of SDP relaxation for QCQPs with bipartite graph structure, 10th International Congress on Industrial and Applied Mathematics, Aug. 2023.
• Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Tight Semidefinite Relaxations for Sign-Indefinite Qcqps with Bipartite Structures, SIAM Conference on Optimization 2023, June 2023.
• Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Exactly Solving a class of QCQPs via Semidefinite Relaxation with Bipartite Sparsity Patterns, International Workshop on Continuous Optimization, Dec. 2022.
• Godai Azuma*, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Exact semidefinite relaxations for QCQPs with forest-structured matrices and its applications, IFORS 2021, Aug. 2021.
• Godai Azuma*, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita. Exactness Conditions for Semidefinite Relaxation of Nonconvex QCQPS with Forest Structures, SIAM Conference on Optimization 2021, July 2021.
• Makoto Yamashita*, Mituhiro Fukuda, Sunyoung Kim, Takashi Nakagaki. A dual spectral projected gradient method for logdeterminant semidefinite problems, ICCOPT 2019, Aug. 2019.
• Mituhiro Fukuda, Takashi Nakagaki, Makoto Yamashita. An efficient nonmonotone spectral projected gradient method for semidefinite program with log-determinant and l1-norm function, Nonlinear Analysis and Convex Analysis 2017, July 2017.
• Makoto Yamashita, Mituhiro Fukuda, Takashi Nakagaki. Dual Approach Based on Spectral Projection Gradient Method for log-det SDP with ell_1 Norm, SIAM Conference on Optimization, May 2014.  公式リンク  
  
• 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, 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.
• Mituhiro Fukuda. Electronic structure calculations using N-representability conditions on second-order reduced density matrices, Workshop on Complex Quantum Information, Mar. 2010.
• Mituhiro Fukuda. Solving large-scale semidefinite programs for the variational calculation of second-order reduced density matrices in fermionic system, Workshop on the Theory of Large Coulomb System, Feb. 2010.
• Mituhiro Fukuda. On the implementation of the primal-dual interior-point method for semidefinite programs with log-determinants, 20th International Symposium on Mathematical Programming, Aug. 2009.
• 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.
• Mituhiro Fukuda. The reduced density matrix method: Applications of the T2' N-representability condition and development of accurate semidefinite solve, Workshop: Mathematical and Algorithmic Challenges in Electronic Structure Theory, Sept. 2008.
• Mituhiro Fukuda. Using a black-box optimization software to determine the second-order reduced density matrices of atoms and molecules by N-representability conditions, Eighth Triennial Congress of the World Association of Theoretical and Computational Chemistry, Sept. 2008.
• Mituhiro Fukuda, Bastiaan J. Braams, Katsuki Fujisawa, Maho Nakata, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao. Approximations of electronic structures of atoms and molecules by semidefinite programming, The 4th Sino-Japanese Optimization Meeting, Aug. 2008.
• Mituhiro Fukuda. Large-scale semidefinite programming applications in theoretical chemistry and data assimilation, VII Brazilian Workshop on Continous Optimization, July 2008.
• Mituhiro Fukuda, Maho Nakata, Makoto Yamashita. Exploiting the semidefinite programming formulation of the variational calculation on second-order reduced density matrix of the atoms and molecules, Odyssey 2008: Mathematical and Computational Aspects of Molecular Electronic Structure Calculation, June 2008.
• Mituhiro Fukuda. Applications of semidefinite programs with log-determinat terms, SIAM Conference on Optimization, May 2008.
• Mituhiro Fukuda, Bastiaan J. Braams, Katsuki Fujisawa, Maho Nakata, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao. Accurate electronic structure calculations using semidefinite programming software, INFORMS Optimization Society: Theory, Computation, and Emerging Applications, Mar. 2008.
• Mituhiro Fukuda. Determination of electronic structure of atoms and molecules using optimization software, The 7th International Conference on Optimization: Techniques and Applications, Dec. 2007.
• Mituhiro Fukuda. Semidefinite programs with log-barrier terms, 2nd Mathematical Programming Society International Conference on Continous Optimization and Modeling and Optimization: Theory and Applications 2007, Aug. 2007.
• Mituhiro Fukuda. Linear semidefinite programs with log-determinant terms, 6th International Congress on Industrial and Applied Mathematics, July 2007.
• Mituhiro Fukuda, Masakazu Kojima, Makoto Yamashita. Prospects on copositive programming, 19th International Symposium on Mathematical Programming, Aug. 2006.
• 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.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel Interior-Point Methods for Large Semi-Definite Programming, SIAM Conference on Parallel Processing for Scientific Computing 2006, Feb. 2006.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. SDPA(SemiDefinite Programming Algorithm) and its Parallel/Completion versions, Informs Annual Meeting 2005, Nov. 2005.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima}. Using the conjugate gradient method in the linear equation for interior-points methods of semidefinite programs, The Second Japanese-Sino Optimization Meeting(JSOM), Sept. 2002.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota. Exploiting Sparsity in Semidefinite Programming via Matrix Completion, The Second International Conference on Nonlinear analysis and Convex Analysis, July 2001.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota. Exploiting Sparsity in Semidefinite Programming via Matrix Completion II: Implementation and Numerical Results, 17th International Symposium on mathematical programming, Aug. 2000.
• Masakazu Kojima, Mituhiro Fukuda, Kazuo Murota, Kazuhide Nakata. Interior-point methods for semidefinite programs using matrix completion, European Conference on Operations Research, July 2000.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Numerical Evaluation of the SDPA (SemiDefinite Programming Algorithm), International workshop on High Performance Optimization Technique, Aug. 1997.

国内会議発表 (査読なし・不明)

• 東悟大*, 福田光浩, Kim Sunyoung, 山下真. 二部グラフで表現可能な疎性を持つ二次制約付き二次計画問題と狭小な半正定値計画緩和の条件, 日本オペレーションズ・リサーチ学会2022春季研究発表会, Mar. 2022.
• 東悟⼤, 福田光浩, 山下真, Sunyoung Kim. 三重対⾓性を持つ⼆次制約付き⼆次計画問題の狭⼩な半正定値計画緩和, 数理最適化の理論・アルゴリズム・応⽤, Aug. 2020.
• Takashi Nakagaki, Mituhiro Fukuda, Makoto Yamashita, Kim Sunyoung. Non-monotone Spectral Projected Gradient Method for Semidefinite Program with Log-Determinant and $\ell_1$-Norm Terms, 高度情報化社会に向けた数理最適化の新潮流, RIMS Kokyuroku Bessatsu, No. 2108, Apr. 2019.
• 福田光浩, 中垣敬, 山下真. 対数行列式とℓ1 ノルム関数をもつ半正定値計画問題に対する, 高度情報化社会に向けた数理最適化の新潮流, Aug. 2018.
• 山下真, 福田光浩, 中垣敬. 対数行列式半正定値計画問題に対する双対スペクトラル射影勾配法の構築, 日本オペレーションズリサーチ学会2014年春季研究発表会, 日本オペレーションズリサーチ学会2014年春季研究発表会アブストラクト集, pp. 238--239, Mar. 2014.
• 金城 憲長, 山下 真, 福田 光浩, 下平 英寿. センサーネットワークモデルにおける重み付けによる数値精度向上について, 日本オペレーションズ・リサーチ学会2012年秋季研究発表会, Sept. 2012.
• 福田光浩, 中田和秀, 藤澤克樹, 山下真. 重み付き対数行列式を持つ半正定値計画問題を解くSDPA, 日本オペレーションズ・リサーチ学会2009年秋季研究発表会, Sept. 2009.
• 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.
• 福田光浩. 半正定値計画方の拡張と新展開ー量子理論よりー, 第19回RAMPシンポジウム, Oct. 2007.
• Mituhiro Fukuda, Masakazu Kojima, Makoto Yamashita. Computational prospects on copositive programming, Modeling and Optimization Theory, July 2006.
• 中田 和秀, 藤沢 克樹, 福田 光浩, 小島 政和, 室田 一雄. 半正定値計画問題に対する行列補完理論の適用, 日本応用数理学会 年会, Oct. 2000.
• Mituhiro Fukuda, Kazuhide Nakata, Katsuki Fujisawa, Masakazu Kojima, Kazuo Murota. Solving Sparse Semidefinite Programs by Matrix Completion (part I), 研究集会「最適化の数理科学」, July 2000.
• 中田 和秀, 藤沢 克樹, 福田 光浩, 小島 政和, 室田 一雄. 行列補完に基づく半正定値計画問題の疎性について, 日本オペレーションズ・リサーチ学会 「最適化とアルゴリズム」研究部会, June 2000.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota. Solving Sparse Semidefinite Programs by Matrix Completion (part II), 京都大学数理解析研究所研究集会 「最適化の数理科学」, 数理解析研究所講究録, Vol. 1174, pp. 130-137, 2000.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota. Matrix Completion and Semidefinite Programming, 統計数理研究所研究集会 最適化：モデリングとアルゴリズム１４, 統計数理研究所共同研究レポート, Vol. 135, pp. 223-237, 2000.

その他の論文・著書など

• 金森敬文, 樺島祥介, 高安美佐子, 中野 張, 福田光浩, 三好直人, 山下 真, 渡邊澄夫. 東京工業大学情報理工学院数理・計算科学系―情報の未来を作り出す数理的アプローチを探究する―, オペレーションズ・リサーチ, Vol. 64, No. 1, pp. 31-32, Jan. 2019.
• 福田光浩, 山下真, 水谷友彦. 国際会議 ICCOPT 2016 Tokyo 開催の経験と教訓 (5) -- プロポーザル作成・会計・アルバイト担当, オペレーションズ・リサーチ, Vol. 61, No. 10, pp. 253--256, Apr. 2017.
• Masaru Ito, Mituhiro Fukuda. A family of subgradient-based methods for convex optimization problems in a unifying framework, Research Report, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, June 2015.
• 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  
  
• FUKUDAMITUHIRO. 半正定値計画問題に対するソルバーの紹介, オペレーションズ・リサーチ : 経営の科学 = [O]perations research as a management science [r]esearch, 公益社団法人日本オペレーションズ・リサーチ学会, Vol. 55, No. 7, pp. 393-399, July 2010.
• 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.
• Mituhiro Fukuda. Semidefinite programming from optimization to quantum chemistry, 東工大クロニクル, Vol. 445, pp. 10-12, July 2009.
• 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.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata, Makoto Yamashita. SDPA-C (SemiDefinite Programming Algorithm -- Completion method) User's Manual --- Version 6.10, Department of Mathematical and Computing Sciences Technical Report, No. 409, 2004.

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