@book{CTT100809058,
  author = {(M.F. Anjos and J.B. Lasserre Ed.) and Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhiro Kobayashi and Kazuhide Nakata and Maho Nakata and (M.F. Anjos and J.B. Lasserre Ed.)},
  title = {Latest developments in the SDPA Family for solving large-scale SDPs},
  publisher = {Springer},
  year = 2011,
}

@book{CTT100552963,
  author = {Mituhiro Fukuda and Maho Nakata and Makoto Yamashita},
  title = {Semidefinite programming: Formulations and primal-dual interior-point methods},
  publisher = {John Wiley & Sons, Inc. (Hoboken)},
  year = 2007,
}

@book{CTT100809059,
  author = {Makoto Yamashita and Mituhiro Fukuda and Katsuki Fujisawa and Masakazu Kojima and Kazuhide Nakata},
  title = {Parallel primal-dual interior-point methods for semidefinite programs},
  publisher = {John Wiley ＆ Sons, Inc},
  year = 2006,
}

@book{CTT100809219,
  author = {Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuhide Nakata},
  title = {Numerical evaluation of the SDPA (semidefinite programming algorithm)},
  publisher = {Springer},
  year = 2000,
}

@article{CTT100884465,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Exact SDP relaxations for quadratic programs with bipartite graph structures},
  journal = {Journal of Global Optimization},
  year = 2022,
}

@article{CTT100866797,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Exact SDP relaxations of quadratically constrained quadratic programs with forest structures},
  journal = {Journal of Global Optimization},
  year = 2022,
}

@article{CTT100820793,
  author = {Takashi Nakagaki and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {A dual spectral projected gradient method for log-determinant semidefinite problems},
  journal = {Computational Optimization and Applications},
  year = 2020,
}

@article{CTT100721088,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Yoshiaki Futakata and Kazuhiro Kobayashi and Kazuhide Nakata and Maho Nakata},
  title = {Parallel solver for SemiDefinite Programming having sparse Schur complement matrix},
  journal = {ACM Transactions on Mathematical Software},
  year = 2012,
}

@article{CTT100773710,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhiro Kobayashi and Kazuhide Nakata and Maho Nakata},
  title = {Latest developments in the SDPA Family for solving large-scale SDPs},
  journal = {Handbook on Semidefinite Cone and Polynomial Optimization},
  year = 2011,
}

@article{CTT100570254,
  author = {Maho Nakata and Bastiaan J. Braams and Mituhiro Fukuda and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  title = {Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver},
  journal = {The Journal of Chemical Physics},
  year = 2008,
}

@article{CTT100553624,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Makoto Yamashita and Maho Nakata and Kazuhiro Kobayashi},
  title = {Optimization Software SDPA},
  journal = {Bulletin of the Japan Society for Industrial and Applied Mathematics},
  year = 2008,
}

@article{CTT100721075,
  author = {Katsuki Fujisawa and Kazuhide Nakata and Makoto Yamashita and Mituhiro Fukuda},
  title = {SDPA Project : Solving Large-scale Semidefinite Programs},
  journal = {Journal of the Operations Research Society of Japan},
  year = 2007,
}

@article{CTT100533159,
  author = {Mituhiro Fukuda and Bastiaan J. Braams and Maho Nakata and Michael L. Overton and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  title = {Large-scale semidefinite programs in electronic structure calculation},
  journal = {Mathematical Programming Series B},
  year = 2007,
}

@article{CTT100773676,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuhide Nakata},
  title = {Parallel primal-dual interior-point methods for semidefinite programs},
  journal = {Parallel Combinatorial Optimization (El-G. Talbi, Ed.)},
  year = 2006,
}

@article{CTT100773677,
  author = {Katsuki Fujisawa and Mituhiro Fukuda and Kazuhide Nakata},
  title = {Preprocessing sparse semidefinite programs via matrix completion},
  journal = {Optimization Methods and Software},
  year = 2006,
}

@article{CTT100533157,
  author = {Maho Nakata and Bastiaan J. Braams and Mituhiro Fukuda and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  title = {Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions},
  journal = {The Journal of Chemical Physics},
  year = 2006,
}

@article{CTT100533155,
  author = {Zhengji Zhao and Bastiaan J. Braams and Mituhiro Fukuda and Michael L. Overton and Jerome K. Percus},
  title = {The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions},
  journal = {The Journal of Chemical Physics},
  year = 2004,
}

@article{CTT100572616,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota},
  title = {Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results},
  journal = {Mathematical Programming},
  year = 2003,
}

@article{CTT100552942,
  author = {Mituhiro Fukuda and Masakazu Kojima and Masayuki Shida},
  title = {Lagrangian dual interior-point methods for semidefinite programs},
  journal = {SIAM Journal on Optimization},
  year = 2002,
}

@article{CTT100574846,
  author = {Maho Nakata and Hiroshi Nakatsuji and Masahiro Ehara and Mituhiro Fukuda and Kazuhide Nakata and Katsuki Fujisawa},
  title = {Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm},
  journal = {The Journal of Chemical Physics},
  year = 2001,
}

@article{CTT100552939,
  author = {Mituhiro Fukuda and Masakazu Kojima},
  title = {Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem},
  journal = {Computational Optimization and Applications},
  year = 2001,
}

@article{CTT100552937,
  author = {Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota and Kazuhide Nakata},
  title = {Exploiting sparsity in semidefinite programming via matrix completion I: General framework},
  journal = {SIAM Journal on Optimization},
  year = 2000,
}

@inproceedings{CTT100902592,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita*},
  title = {Tightness conditions of SDP relaxation for QCQPs with bipartite graph structure},
  booktitle = {},
  year = 2023,
}

@inproceedings{CTT100891946,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Tight Semidefinite Relaxations for Sign-Indefinite Qcqps with Bipartite Structures},
  booktitle = {},
  year = 2023,
}

@inproceedings{CTT100884466,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Exactly Solving a class of QCQPs via Semidefinite Relaxation with Bipartite Sparsity Patterns},
  booktitle = {},
  year = 2022,
}

@inproceedings{CTT100867384,
  author = {Godai Azuma and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {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},
  booktitle = {},
  year = 2022,
}

@inproceedings{CTT100861287,
  author = {Godai Azuma* and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Exact semidefinite relaxations for QCQPs with forest-structured matrices and its applications},
  booktitle = {},
  year = 2021,
}

@inproceedings{CTT100858536,
  author = {Godai Azuma* and Mituhiro Fukuda and Sunyoung Kim and Makoto Yamashita},
  title = {Exactness Conditions for Semidefinite Relaxation of Nonconvex QCQPS with Forest Structures},
  booktitle = {},
  year = 2021,
}

@inproceedings{CTT100830796,
  author = {Godai Azuma and Mituhiro Fukuda and Makoto Yamashita and Sunyoung Kim},
  title = {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},
  booktitle = {},
  year = 2020,
}

@inproceedings{CTT100803082,
  author = {Makoto Yamashita* and Mituhiro Fukuda and Sunyoung Kim and Takashi Nakagaki},
  title = {A dual spectral projected gradient method for logdeterminant semidefinite problems},
  booktitle = {},
  year = 2019,
}

@inproceedings{CTT100799612,
  author = {Takashi Nakagaki and Mituhiro Fukuda and Makoto Yamashita and Kim Sunyoung},
  title = {Non-monotone Spectral Projected Gradient Method for Semidefinite Program with Log-Determinant and $\ell_1$-Norm Terms},
  booktitle = {RIMS Kokyuroku Bessatsu},
  year = 2019,
}

@inproceedings{CTT100770344,
  author = {Mituhiro Fukuda and Takashi Nakagaki and Makoto Yamashita},
  title = {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},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100747640,
  author = {Mituhiro Fukuda and Takashi Nakagaki and Makoto Yamashita},
  title = {An efficient nonmonotone spectral projected gradient method for semidefinite program with log-determinant and l1-norm function},
  booktitle = {},
  year = 2017,
}

@inproceedings{CTT100672778,
  author = {Makoto Yamashita and Mituhiro Fukuda and Takashi Nakagaki},
  title = {Dual Approach Based on Spectral Projection Gradient Method for log-det SDP with ell_1 Norm},
  booktitle = {},
  year = 2014,
}

@inproceedings{CTT100667862,
  author = {Makoto Yamashita and Mituhiro Fukuda and Takashi Nakagaki},
  title = {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},
  booktitle = {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},
  year = 2014,
}

@inproceedings{CTT100691749,
  author = {Maho Nakata and Mituhiro Fukuda and Katsuki Fujisawa},
  title = {Variational approach to electronic structure calculations on second-order reduced density matrices and the N-representability problem},
  booktitle = {in Complex Quantum Systems: Analysis of Large Coulomb Systems (H. Siedentop, ed.), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore},
  year = 2013,
}

@inproceedings{CTT100654956,
  author = {金城 憲長 and 山下 真 and 福田 光浩 and 下平 英寿},
  title = {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},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100654935,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhide Nakata and Maho Nakata},
  title = {Parallel Computation for SDPs Focusing on the Sparsity of Schur Complements Matrices},
  booktitle = {},
  year = 2011,
}

@inproceedings{CTT100654926,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhide Nakata and Maho Nakata},
  title = {High Performance Solvers for Semidefinite Programs},
  booktitle = {Proceedings of the Korean Society for Industrial and Appplied Mathematcis},
  year = 2011,
}

@inproceedings{CTT100615188,
  author = {Mituhiro Fukuda},
  title = {Electronic structure calculations using N-representability conditions on second-order reduced density matrices},
  booktitle = {},
  year = 2010,
}

@inproceedings{CTT100615187,
  author = {Mituhiro Fukuda},
  title = {Solving large-scale semidefinite programs for the variational calculation of second-order reduced density matrices in fermionic system},
  booktitle = {},
  year = 2010,
}

@inproceedings{CTT100806354,
  author = {Mituhiro Fukuda and Kazuhide Nakata and Katsuki Fujisawa and Makoto Yamashita},
  title = {重み付き対数行列式を持つ半正定値計画問題を解くSDPA},
  booktitle = {},
  year = 2009,
}

@inproceedings{CTT100615186,
  author = {Mituhiro Fukuda},
  title = {On the implementation of the primal-dual interior-point method for semidefinite programs with log-determinants},
  booktitle = {},
  year = 2009,
}

@inproceedings{CTT100863988,
  author = {Katsuki Fujisawa and MASAKAZU KOJIMA and Kazuhide Nakata and Mituhiro Fukuda and Makoto Yamashita and Maho Nakata},
  title = {SDPA project and new features of SDPA 7.1.0},
  booktitle = {数理解析研究所講究録},
  year = 2008,
}

@inproceedings{CTT100575768,
  author = {Makoto Yamashita and Mituhiro Fukuda and Masakazu Kojima and Kazuhide Nakata and Katsuki Fujisawa and Kazuhiro Kobayashi and Maho Nakata},
  title = {SDPA: Leading-edge software for SDP},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575126,
  author = {Mituhiro Fukuda},
  title = {The reduced density matrix method: Applications of the T2' N-representability condition and development of accurate semidefinite solve},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575127,
  author = {Mituhiro Fukuda},
  title = {Using a black-box optimization software to determine the second-order reduced density matrices of atoms and molecules by N-representability conditions},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575142,
  author = {Mituhiro Fukuda and Bastiaan J. Braams and Katsuki Fujisawa and Maho Nakata and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  title = {Approximations of electronic structures of atoms and molecules by semidefinite programming},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575129,
  author = {Mituhiro Fukuda},
  title = {Large-scale semidefinite programming applications in theoretical chemistry and data assimilation},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575442,
  author = {Mituhiro Fukuda and Maho Nakata and Makoto Yamashita},
  title = {Exploiting the semidefinite programming formulation of the variational calculation on second-order reduced density matrix of the atoms and molecules},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575131,
  author = {Mituhiro Fukuda},
  title = {Applications of semidefinite programs with log-determinat terms},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575144,
  author = {Mituhiro Fukuda and Bastiaan J. Braams and Katsuki Fujisawa and Maho Nakata and Jerome K. Percus and Makoto Yamashita and Zhengji Zhao},
  title = {Accurate electronic structure calculations using semidefinite programming software},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100575133,
  author = {Mituhiro Fukuda},
  title = {Determination of electronic structure of atoms and molecules using optimization software},
  booktitle = {},
  year = 2007,
}

@inproceedings{CTT100575124,
  author = {Mituhiro Fukuda},
  title = {半正定値計画方の拡張と新展開ー量子理論よりー},
  booktitle = {},
  year = 2007,
}

@inproceedings{CTT100575134,
  author = {Mituhiro Fukuda},
  title = {Semidefinite programs with log-barrier terms},
  booktitle = {},
  year = 2007,
}

@inproceedings{CTT100575135,
  author = {Mituhiro Fukuda},
  title = {Linear semidefinite programs with log-determinant terms},
  booktitle = {},
  year = 2007,
}

@inproceedings{CTT100575145,
  author = {Mituhiro Fukuda and Masakazu Kojima and Makoto Yamashita},
  title = {Prospects on copositive programming},
  booktitle = {},
  year = 2006,
}

@inproceedings{CTT100575141,
  author = {Mituhiro Fukuda and Masakazu Kojima and Makoto Yamashita},
  title = {Computational prospects on copositive programming},
  booktitle = {},
  year = 2006,
}

@inproceedings{CTT100654944,
  author = {Makoto Yamashita and Mituhiro Fukuda and Katsuki Fujisawa and Masakazu Kojima and Kazuhide Nakata and Maho Nakata},
  title = {Large-scale semidefinite programming from quantum chemistry},
  booktitle = {},
  year = 2006,
}

@inproceedings{CTT100654948,
  author = {Makoto Yamashita and Mituhiro Fukuda and Katsuki Fujisawa and Masakazu Kojima and Kazuhide Nakata},
  title = {Parallel Interior-Point Methods for Large Semi-Definite Programming},
  booktitle = {},
  year = 2006,
}

@inproceedings{CTT100654949,
  author = {Makoto Yamashita and Mituhiro Fukuda and Katsuki Fujisawa and Masakazu Kojima and Kazuhide Nakata},
  title = {SDPA(SemiDefinite Programming Algorithm) and its Parallel/Completion versions},
  booktitle = {},
  year = 2005,
}

@inproceedings{CTT100806098,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima}},
  title = {Using the conjugate gradient method in the linear equation for interior-points methods of semidefinite programs},
  booktitle = {},
  year = 2002,
}

@inproceedings{CTT100806099,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota},
  title = {Exploiting Sparsity in Semidefinite Programming via Matrix Completion},
  booktitle = {},
  year = 2001,
}

@inproceedings{CTT100806320,
  author = {Kazuhide Nakata and 藤沢 克樹 and Mituhiro Fukuda and MASAKAZU KOJIMA and Kazuo Murota},
  title = {半正定値計画問題に対する行列補完理論の適用},
  booktitle = {},
  year = 2000,
}

@inproceedings{CTT100806101,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota},
  title = {Exploiting Sparsity in Semidefinite Programming via Matrix Completion II: Implementation and Numerical Results},
  booktitle = {},
  year = 2000,
}

@inproceedings{CTT100806331,
  author = {Masakazu Kojima and Mituhiro Fukuda and Kazuo Murota and Kazuhide Nakata},
  title = {Interior-point methods for semidefinite programs using matrix completion},
  booktitle = {},
  year = 2000,
}

@inproceedings{CTT100806324,
  author = {Mituhiro Fukuda and Kazuhide Nakata and Katsuki Fujisawa and Masakazu Kojima and Kazuo Murota},
  title = {Solving Sparse Semidefinite Programs by Matrix Completion (part I)},
  booktitle = {},
  year = 2000,
}

@inproceedings{CTT100806319,
  author = {Kazuhide Nakata and 藤沢 克樹 and Mituhiro Fukuda and MASAKAZU KOJIMA and Kazuo Murota},
  title = {行列補完に基づく半正定値計画問題の疎性について},
  booktitle = {},
  year = 2000,
}

@inproceedings{CTT100773717,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota},
  title = {Solving Sparse Semidefinite Programs by Matrix Completion (part II)},
  booktitle = {数理解析研究所講究録},
  year = 2000,
}

@inproceedings{CTT100773715,
  author = {Kazuhide Nakata and Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota},
  title = {Matrix Completion and Semidefinite Programming},
  booktitle = {統計数理研究所共同研究レポート},
  year = 2000,
}

@inproceedings{CTT100552929,
  author = {Akiko Takeda and Yang Dai and Mituhiro Fukuda and Masakazu Kojima},
  title = {Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems},
  booktitle = {Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems (P. M. Pardalos, Ed.)},
  year = 2000,
}

@inproceedings{CTT100809218,
  author = {Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuhide Nakata},
  title = {Numerical Evaluation of the SDPA (SemiDefinite Programming Algorithm)},
  booktitle = {},
  year = 1997,
}

@misc{CTT100785189,
  author = {takafumi kanamori and YOSHIYUKI KABASHIMA and Misako Takayasu and Yumiharu Nakano and Mituhiro Fukuda and Naoto Miyoshi and Makoto Yamashita and SUMIO WATANABE},
  title = {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―},
  year = 2019,
}

@misc{CTT100738420,
  author = {Mituhiro Fukuda and Makoto Yamashita and TOMOHIKO MIZUTANI},
  title = {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},
  year = 2017,
}

@misc{CTT100691747,
  author = {Masaru Ito and Mituhiro Fukuda},
  title = {A family of subgradient-based methods for convex optimization problems in a unifying framework},
  year = 2015,
}

@misc{CTT100773674,
  author = {Makoto Yamashita and Katsuki Fujisawa and Mituhiro Fukuda and Kazuhide Nakata and Maho Nakata},
  title = {Parallel Computing for Large-scale Semidefinite Programs},
  year = 2013,
}

@misc{CTT100791590,
  author = {MITUHIRO FUKUDA},
  title = {半正定値計画問題に対するソルバーの紹介},
  year = 2010,
}

@misc{CTT100809222,
  author = {Makoto Yamashita and Katsuki Fujisawa and Kazuhide Nakata and Maho Nakata and Mituhiro Fukuda and Kazuhiro Kobayashi and Kazushige Goto},
  title = {A high-performance software package for semidefinite programs: SDPA 7},
  year = 2010,
}

@misc{CTT100615184,
  author = {Mituhiro Fukuda},
  title = {Semidefinite programming from optimization to quantum chemistry},
  year = 2009,
}

@misc{CTT100806344,
  author = {Katsuki Fujisawa and Mituhiro Fukuda and Kazuhiro Kobayashi and Masakazu Kojima and Kazuhide Nakata and Maho Nakata and Makoto Yamashita},
  title = {SDPA (SemiDefinite Programming Algorithm) User's Manual --- Version 7.0.5},
  year = 2008,
}

@misc{CTT100806343,
  author = {Katsuki Fujisawa and Mituhiro Fukuda and Masakazu Kojima and Kazuhide Nakata and Makoto Yamashita},
  title = {SDPA-C (SemiDefinite Programming Algorithm -- Completion method) User's Manual --- Version 6.10},
  year = 2004,
}