A. Research Reports

B. Journal Articles

C. Refereed Conference Proceedings

D. Refereed Book Chapters

E. Non-Refereed Book Chapters

F. Unpublished Research Reports

G. Other Publications

H. Doctoral Thesis

I. Master Thesis

J. Productivity Indicators

1. M. Yamashita, K. Fujisawa, K. Nakata, M. Nakata, M. Fukuda, K. Kobayashi, and K. Goto, "A high-performance software package for semidefinite programs: SDPA 7," Research Report B-460, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, January 2010.

1. M. Yamashita, K. Fujisawa, M. Fukuda, K. Nakata, and M. Nakata, "Parallel solver for semidefinite programming problem having sparse Schur complement matrix," Research Report B-463, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, September 2010, revised August 2011. To appear in ACM Transactions on Mathematical Software.
   
   
2. M. Nakata, B. J. Braams, K. Fujisawa, M. Fukuda, J. K. Percus, M. Yamashita, and Z. 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, 128 (2008), 164113.
   
   
3. K. Nakata, K. Fujisawa, M. Fukuda, M. Yamashita, M. Nakata, and K. Kobayashi, "Optimization software SDPA," Bulletin of the Japan Society for Industrial and Applied Mathematics, 18 (2008), pp. 2-14 (in Japanese).
   
   
4. K. Fujisawa, K. Nakata, M. Yamashita, and M. Fukuda, "SDPA project: Solving large-scale semidefinite programs," Journal of the Operations Research Society of Japan, 50 (2007), pp. 278-298.
   
   
5. M. Fukuda, B. J. Braams, M. Nakata, M. L. Overton, J. K. Percus, M. Yamashita, and Z. Zhao, "Large-scale semidefinite programs in electronic structure calculation," Mathematical Programming, Series B, 109 (2007), pp. 553-580.
   
   
6. M. Nakata, B. J. Braams, M. Fukuda, J. K. Percus, M. Yamashita, and Z. 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, 125 (2006), 244109.
   
   
7. K. Fujisawa, M. Fukuda, and K. Nakata, "Preprocessing sparse semidefinite programs via matrix completion," Optimization Methods and Software, 21 (2006), pp. 17-39.
   
   
8. Z. Zhao, B. J. Braams, M. Fukuda, M. L. Overton, and J. K. Percus, "The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions," The Journal of Chemical Physics, 120 (2004), pp. 2095-2104.
   
   
9. K. Nakata, K. Fujisawa, M. Fukuda, M. Kojima, and K. Murota, "Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results," Mathematical Programming, Series B, 95 (2003), pp. 303-327.
   
   
10. M. Fukuda, M. Kojima, and M. Shida, "Lagrangian dual interior-point methods for semidefinite programs," SIAM Journal on Optimization, 12 (2002), pp. 1007-1031.
    
    
11. M. Fukuda and M. Kojima, "Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem," Computational Optimization and Applications, 19 (2001), pp. 79-105.
    
    
12. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, "Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm," The Journal of Chemical Physics, 114 (2001), pp. 8282-8292.
    
    
13. M. Fukuda, M. Kojima, K. Murota, and K. Nakata, "Exploiting sparsity in semidefinite programming via matrix completion I: General framework," SIAM Journal on Optimization, 11 (2000), pp. 647-674.

1. M. Nakata, M. Fukuda, and K. Fujisawa, "Variational approach forthe electronic structure calculation on the second-order reduced density matrices and the N-representability problem," arXiv 1010.4095, 20 October 2010, revised 24 June 2011. To appear in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore.
   
   
2. A. Takeda, Y. Dai, M. Fukuda, and M. Kojima, "Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems," in Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, P. M. Pardalos, ed., (Kluwer Academic Publishers, Dordrecht, 2000), pp. 489-510.
   
   
3. K. Fujisawa, M. Fukuda, M. Kojima, and K. Nakata, "Numerical evaluation of SDPA (SemiDefinite Programming Algorithm)," in High Performance Optimization, H. Frenk, K. Roos, T. Terlaky, and S. Zhang, eds., (Kluwer Academic Publishers, Dordrecht, 2000), pp. 267-301.

1. M. Fukuda, B. J. Braams, M. Nakata, M. L. Overton, J. K. Percus, M. Yamashita, and Z. Zhao, "Large-scale semidefinite programs in electronic structure calculation," Research Report B-413, February 2005. A revised short version is here.
   
   
2. M. Fukuda, M. Kojima, and M. Shida, "Lagrangian dual interior-point methods for semidefinite programs," Research Report B-369, March 2001. A revised short version is here.
   
   
3. M. Shida, "An interior-point smoothing techniques for Lagrange relaxation in convex programing," Working Paper, April 1998.

1. M. Fukuda, M. Yamashita, and M. Kojima, "Computational prospects on copositive programming," RIMS Kôkyûroku, 1526 (2006), pp. 207-213.
   
   
2. M. Fukuda, B. J. Braams, M. Nakata, M. L. Overton, J. K. Percus, M. Yamashita, and Z. Zhao, "Semidefinite programs in electronic structure calculation," RIMS Kôkyûroku, 1461 (2005), pp. 15-29.
   
   
3. K. Nakata, K. Fujisawa, M. Fukuda, M. Kojima, and K. Murota, "Solving sparse semidefinite programs by matrix completion (part II)," RIMS Kôkyûroku, 1174 (2000), pp. 130-137.
   
   
4. M. Fukuda, K. Nakata, K. Fujisawa, M. Kojima, and K. Murota, "Solving sparse semidefinite programs by matrix completion (part I)," RIMS Kôkyûroku, 1174 (2000), pp. 122-129.
   
   
5. M. Fukuda and M. Kojima, "Approximation of global optimal values of nonconvex programs using successive convex relaxation method," RIMS Kôkyûroku, 1114 (1999), pp. 67-73.

• M. Fukuda, Sparsity Techniques in Interior-Point Methods for Semidefinite Programming, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, April 2002.

• M. Fukuda, Branch-and-Cut Algorithms for Bilinear Matrix Inequality Problems, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, February 1999.