論文

• Kazuo Murota, Akiyoshi Shioura. On Equivalence of M^\natural-concavity of a Set Function and Submodularity of its Conjugate, Journal of Operations Research Society of Japan, Vol. 61, pp. 163-171, Apr. 2018.
• Kazuo Murota, Akiyoshi Shioura. Simpler Exchange Axioms for M-concave Functions on Generalized Polymatroids, Japan Journal of Industrial and Applied Mathematics (JJIAM), Vol. 35, pp. 235-259, Dec. 2017.
• Kazuo Murota, Akiyoshi Shioura. Note on time bounds of two-phase algorithms for L-convex function minimization, Japan Journal of Industrial and Applied Mathematics (JJIAM), Vol. 34, pp. 429-440, May 2017.
• Kazuo Murota, Yoshihiro Kanno, MASAKAZU KOJIMA, SADAYOSHI KOJIMA. A numerical algorithm for block-diagonal decomposition of matrix *-algebras, Part I: proposed approach and application to semidefinite programming, Japan Journal of Industrial and Applied Mathematics, Vol. 27, pp. 125-160, Oct. 2010.
• 田中健一郎, 杉原正顕, 室田一雄. Error Estimate of a Gaussian Kernel Sampling Formula via Complex Analysis, Transactions of the Japan Society for Industrial and Applied Mathematics, 2007.
• Kazuo Murota, Ken'ichiro Tanaka. A Steepest Descent Algorithm for M-Convex Functions on Jump Systems, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E89-A, No. 5, pp. 1160-1165, May 2006.
• 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, 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.

国際会議発表 (査読なし・不明)

• 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.

国内会議発表 (査読なし・不明)

• 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. 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.
• 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.

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