論文

• Mirai TANAKA, Kazuhide Nakata, hayato waki. Numerical reduction method for doubly nonnegative optimization problems, Journal of Math-for-Industry, Vol. 5, pp. 41--50, 2013.
• Sunyoung Kim, Masakazu Kojima, Hayato Waki, Makoto Yamashita. Algorithm 920: SFSDP: a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems, Transactions on Mathematical Software, ACM, Aug. 2012.  公式リンク  
  
• Mirai TANAKA, Kazuhide Nakata, hayato waki. 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, Pacific Journal of Optimization, Vol. 8, pp. 699-724, 2012.
• H. Waki, S. Kim, M. Kojima, M. Muramatsu. Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity, SIAM Journal on Optimization, Vol. SIAM Journal on Optimization, No. 1, pp. 218-242, 2006.
• Masakazu Kojima, Sunyoung Kim, Hayato Waki. Sparsity in Sums of Squares of Polynomials, Mathematical Programming, Vol. 103, No. 1, pp. 45-62, Apr. 2005.
• S. Kim, M. Kojima, H. Waki. Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems, SIAM Journal on Optimization, Vol. 15, No. 3, pp. 697-719, 2005.
• Masakazu Kojima, Sunyoung Kim, Hayato Waki. A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones, Journal of Operations Research Society of Japan, Vol. 46, No. 2, pp. 125-144, Feb. 2003.

国際会議発表 (査読有り)

• Katsuki Fujisawa, Toshio Endo, Yuichiro Yasui, Hitoshi Sato, Naoki Matsuzawa, Satoshi Matsuoka, Hayato Waki. Peta-scale General Solver for Semidefinite Programming Problems with over Two Million Constraints, IEEE International Conference on Parallel and Distributed Processing Symposium 2014 (IPDPS2014), Proc. of IEEE International Conference on Parallel and Distributed Processing Symposium 2014 (IPDPS2014), pp. 1171-1180, May 2014.

国際会議発表 (査読なし・不明)

• Mirai Tanaka, Kazuhide Nakata, Hayato Waki. Numerical computation of a facial reduction algorithm for doubly nonnegative optimization problems, INFORMS Annual Meeting 2012, Oct. 2012.
• Mirai Tanaka, Kazuhide Nakata, Hayato Waki. Numerical computation of a facial reduction algorithm and an inexact primal-dual path-following method for doubly nonnegative optimization problems,, 21st International Symposium on Mathematical Programming, Aug. 2012.
• Mirai Tanaka, Kazuhide Nakata, Hayato Waki. An effective approach for DNN relaxation problems for mixed binary nonconvex quadratic optimization,, INFORMS Optimization Society Conference 2012, Feb. 2012.

国内会議発表 (査読なし・不明)

• 田中未来, 中田和秀, 脇隼人. 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, 2012 年度 数値解析研究集会, Sept. 2012.
• 田中未来, 中田和秀, 脇隼人. 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, 日本オペレーションズ・リサーチ学会 最適化の理論と応用研究部会 SOTA@つくば, July 2012.
• 田中未来, 中田和秀, 脇隼人. 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, 京都大学数理解析研究所研究集会 最適化手法の深化と広がり,, 京都大学数理解析研究所講究録, Vol. 1773, pp. 186-197, 2012.
• 田中未来, 中田和秀, 脇隼人. 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, 日本オペレーションズ・リサーチ学会 2011 年秋季研究発表会, Sept. 2011.
• 田中未来, 中田和秀, 脇隼人. 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, 日本オペレーションズ・リサーチ学会 2011 年春季研究発表会, Mar. 2011.

その他の論文・著書など

• 小島政和, 脇隼人. 多項式最適化問題に対する半正定値計画緩和, システム／制御／情報, Vol. 48, No. 12, pp. 477-482, Dec. 2004.

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