@article{CTT100721059,
  author = {Mirai TANAKA and Kazuhide Nakata and hayato waki},
  title = {Numerical reduction method for doubly nonnegative optimization problems},
  journal = {Journal of Math-for-Industry},
  year = 2013,
}

@article{CTT100654902,
  author = {Sunyoung Kim and Masakazu Kojima and Hayato Waki and Makoto Yamashita},
  title = {Algorithm 920: SFSDP: a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems},
  journal = {Transactions on Mathematical Software},
  year = 2012,
}

@article{CTT100721065,
  author = {Mirai TANAKA and Kazuhide Nakata and hayato waki},
  title = {Application of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative relaxation for mixed binary nonconvex quadratic optimization problems},
  journal = {Pacific Journal of Optimization},
  year = 2012,
}

@article{CTT100529489,
  author = {H. Waki and S. Kim and M. Kojima and M. Muramatsu},
  title = {Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity},
  journal = {SIAM Journal on Optimization},
  year = 2006,
}

@article{CTT100392545,
  author = {Masakazu Kojima and Sunyoung Kim and Hayato Waki},
  title = {Sparsity in Sums of Squares of Polynomials},
  journal = {Mathematical Programming},
  year = 2005,
}

@article{CTT100408225,
  author = {S. Kim and M. Kojima and H. Waki},
  title = {Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems},
  journal = {SIAM Journal on Optimization},
  year = 2005,
}

@article{CTT100392534,
  author = {Masakazu Kojima and Sunyoung Kim and Hayato Waki},
  title = {A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones},
  journal = {Journal of Operations Research Society of Japan},
  year = 2003,
}

@inproceedings{CTT100687007,
  author = {Katsuki Fujisawa and Toshio Endo and Yuichiro Yasui and Hitoshi Sato and Naoki Matsuzawa and Satoshi Matsuoka and Hayato Waki},
  title = {Peta-scale General Solver for Semidefinite Programming Problems with over Two Million Constraints},
  booktitle = {Proc. of IEEE International Conference on Parallel and Distributed Processing Symposium 2014 (IPDPS2014)},
  year = 2014,
}

@inproceedings{CTT100805029,
  author = {Mirai Tanaka and Kazuhide Nakata and Hayato Waki},
  title = {Numerical computation of a facial reduction algorithm for doubly nonnegative optimization problems},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100806123,
  author = {田中未来 and 中田和秀 and 脇隼人},
  title = {非負半正定値最適化問題に対する主双対パス追跡法における探索方向の計算},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100805510,
  author = {Mirai Tanaka and Kazuhide Nakata and Hayato Waki},
  title = {Numerical computation of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative optimization problems,},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100806360,
  author = {田中未来 and 中田和秀 and 脇隼人},
  title = {非負半正定値最適化問題に対する面的縮小法の数値計算と主双対内点法},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100805971,
  author = {Mirai Tanaka and Kazuhide Nakata and Hayato Waki},
  title = {An effective approach for DNN relaxation problems for mixed binary nonconvex quadratic optimization,},
  booktitle = {},
  year = 2012,
}

@inproceedings{CTT100773712,
  author = {田中未来 and 中田和秀 and 脇隼人},
  title = {0-1 整数変数を含む非凸 2 次最適化問題の非負半正定値緩和に対する面的縮小と効率的解法},
  booktitle = {京都大学数理解析研究所講究録},
  year = 2012,
}

@inproceedings{CTT100806125,
  author = {田中未来 and 中田和秀 and 脇隼人},
  title = {面的縮小を施した非負半正定値最適化問題に対する主双対パス追跡法の探索方向},
  booktitle = {},
  year = 2011,
}

@inproceedings{CTT100806127,
  author = {田中未来 and 中田和秀 and 脇隼人},
  title = {0-1 整数変数を含む非凸 2 次最適化問題に対する面的縮小を用いた非負半正定値緩和},
  booktitle = {},
  year = 2011,
}

@misc{CTT100392540,
  author = {小島政和 and 脇隼人},
  title = {多項式最適化問題に対する半正定値計画緩和},
  year = 2004,
}