論文

• Masakazu Kojima, Makoto Yamashita. Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization, Mathematical Programming, Springer, Vol. 138, No. 1-2, pp. 333-364, Apr. 2013.  公式リンク  
  
• 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  
  
• Sunyoung Kim, Masakazu Kojima, Martin Mevissen, Makoto Yamashita. Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion, Mathematical Programming, Springer, Vol. 129, No. 1, pp. 33--68, Sept. 2011.  公式リンク  
  
• 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.
• SUNYOUNG KIM, MASAKAZU KOJIMA，HAYATO WAKI. Exploiting Sparsity in SDP Relaxation for Sensor Network Localization, SIAM Journal of Optimization, Vol. 20, No. 1, pp. 192-215, Feb. 2010.
• Martin Mevissen, MASAKAZU KOJIMA. SDP Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems, Asia-Pacific Journal of Operational Research, Vol. 27, No. 1, pp. 15-38, Feb. 2010.
• MASAKAZU KOJIMA. SDP Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems, Asia-Pacific Journal of Operational Research, Vol. 27, No. 1, pp. 15-38, Feb. 2010.
• HAYATO WAKI, MASASKAZU MURAMATSU, MASAKAZU KOJIMA. Invariance under Affine Transformation in Semidefinite Programming Relaxation for Polynomial Optimization Problems, Pacific Journal of Optimization, Vol. 5, No. 2, pp. 297-312, Feb. 2010.
• SUNYOUNG KIM, MASAKAZU KOJIMA. Solving polynomial least squares problems via semidefinite programming relaxations, Journal of Global Optimization, Vol. 46, No. 1, pp. 1-23, Jan. 2010.
• Kazuo Murota, Yoshio Kanno, Masakazu Kojima, Sadayoshi Kojima. A numerical algorithm for block-diagonal decomposition of matrix *-algebra, Japan Journal of Industrial and Applied Mathematics, 2010.
• sunyoung kim, MASAKAZU KOJIMA, Philip Toint. Recognizing Underlying Sparsity in Optimization, Mathematical Programming, Vol. 119, No. 2, pp. 273-303, July 2009.
• Masakazu Kojima, Masakazu Muramatsu. A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones, Computational Optimization and Applications, Vol. 42, No. 1, pp. 31-41, Jan. 2009.
• 鈴木 健太郎, 三好 直人, 小島 政和. 拡散過程の生存確率に対する半正定値計画を用いた数値計算手法, 日本オペレーションズ・リサーチ学会和文論文誌, vol. 51, pp. 25-43, Dec. 2008.
• Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu, H. Sugimoto. SparsePOP : A sparse semidefinite programming relaxation of polynomial optimization problems, ACM Transactions on Mathematical Software, Vol. 35, No. 2, pp. 15-, Nov. 2008.
• Kazuhiro Kobayashi, Sunyoung Kim, Masakazu Kojima. Sparse second order cone programming formulations for convex optimization problems, Journal of the Operations Research Society of Japan, Vol. 51, No. 3, pp. 241-264, Sept. 2008.
• Kazuhiro Kobayashi, Sunyoung Kim, MASAKAZU KOJIMA. Sparse Second Order Cone Programming Formulations for Conves Optimization Problems, Journal of the Operations Research Society of Japan, Vol. 51, No. 3, pp. 241-264, Sept. 2008.
• Kazuhiro Kobayashi, Sunyoung Kim, Masakazu Kojima. Correlative sparsity in primal-dual interior-point methods for LP, SDP and SOCP, Applied Mathematics and Optimization, Vol. 58, No. 1, pp. 69-88, Aug. 2008.
• Martin Mevissen, Masakazu Kojima, Jiawang Nie, Nobuki Takayama. Solving partial differential equations via sparse SDP relaxations, Pacific Journal of Optimization, Vol. 4, No. 2, pp. 213-241, May 2008.
• Cong Vo, Masakazu Muramatsu, Masakazu Kojima. Equality based contraction of semidefinite programming relaxations in polynomial optimization, Journal of the Operations Research Society of Japan, Vol. 51, No. 1, pp. 111-125, Mar. 2008.
• Masakazu Kojima. Efficient evaluation of polynomials and their partial derivatives in homotopy continuation methods, Journal of the Operations Research Society of Japan, Vol. 51, No. 1, pp. 29-54, Mar. 2008.
• Masakazu Kojima, Masakazu Muramatsu. An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones, Mathematical Programming, Vol. 110, No. 2, pp. 315-336, July 2007.
• 水谷友彦, 武田朗子, 小島政和. Dynamic Enumeration of All Mixed Cells, Discrete and Computational Geometry, Vol. 37, No. 3, pp. 351-367, May 2007.
• Tomohiko Mizutani, Akiko Takeda, Masakazu Kojima. Dynamic enumeration of all mixed cells, Discrete & Computational Geometry, Vol. 37, No. 3, pp. 351-367, 2007.
• Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Parallel primal-dual interior-point methods for semidefinite programs, Parallel Combinatorial Optimization (El-G. Talbi, Ed.), John Wiley & Sons, Inc. (Hoboken), Vol. 32, No. 1, pp. 211-238, Oct. 2006.
• T. Gunji, S. Kim, K. Fujisawa, M. Kojima. PHoMpara -- Parallel Implementation of the Polyhedral Homotopy Continuation Method, Computing, Vol. 77, No. 4, pp. 387-411, 2006.
• 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. 17, pp. 218-242, 2006.
• 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.
• M. Kojima, S. Kim, H. Waki. Sparsity in Sums of Squares of Polynomials, Mathematical Programming, Vol. 103, No. 1, pp. 45-62, 2005.
• Cong Vo, Akiko Takeda, Masakazu Kojima. A Multilevel Parallelized Brancd and Bound Hybrid Algorithm for Quadratic Optimization, IPSJ Transactions on Advanced Computing Systems, Vol. 45, No. SIG 6(ACS 6), pp. 186-196, 2004.
• Takayuki Gunji, Sunyoung Kim, Masakazu Kojima, Akiko Takeda, Katsuki Fujisawa, Tomohiko Mizutani. PHoM -- a Polyhedral Homotopy Continuation Method, Computing, Vol. 73, No. 1, pp. 55-77, 2004.
• 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. 2, pp. 477-482, 2004.
• K. Fujisawa, M. Kojima, A. Takeda, M. Yamashita. Solving Large Scale Optimization Problems via Grid and Cluster Computing, Journal of Operations Research Society of Japan, Vol. 47, No. 4, pp. 265-274, 2004.
• Sunyoung Kim, Masakazu Kojima. Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods, Computing, Vol. 73, No. 4, pp. 329-348, 2004.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima. SDPARA : SemiDefinite Programming Algorithm PARAllel Version, Parallel Computing, Vol. 29, No. 8, pp. 1053-1067, 2003.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima. Implementation and Evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0), Optimization Methods and Software , Vol. 18, No. 4, pp. 491-505, 2003.
• Sunyoung Kim, Masakazu Kojima. Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations, Computational Optimization and Applications , Vol. 26, No. 2, pp. 143-154, 2003.
• Sunyoung Kim, Masakazu Kojima, Makoto Yamashita. Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint, Optimization Methods and Software, Vol. 18, No. 5, pp. 535-541, 2003.
• Yang Dai, Sunyoung Kim, Masakazu Kojima. Computing All Nonsingular Solutions of Cyclic-n Polynomial Using Polyhedral Homotopy Continuation Methods, Journal of Computational and Applied Mathematics, Vol. 152, No. 1-2, pp. 83-97, 2003.
• 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, 2003.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima. Implementaion and Evaluation of SDPA 6.0, Optimization Methods and Software, Vol. 18, No. 4, pp. 491-505, 2003.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima. SDPARA: SemiDefinite Programming Algorithm PARAllel Version, Parallel Computing, Vol. 29, No. 8, pp. 1053-1067, 2003.
• Sunyoung Kim, Masakazu Kojima, Makoto Yamashita. Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint, Optimization Methods and Software, Vol. 18, No. 5, pp. 535-541, 2003.
• 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.
• Masakazu Kojima, Levent Tuncel. On the Finite Convergence of Successive SDP Relaxation Methods, European Journal of Operations Research, Vol. 143, No. 2, pp. 325-341, 2002.
• Kim-Chuan Toh, Masakazu Kojima. Solving 　Ｓome Large Scale Semidenite Programs via the Conjugate Residual Method, SIAM Journal on Optimization, Vol. 12, No. 3, pp. 669-691, 2002.
• Akiko Takeda, Katsuki Fujisawa, Yusuke Fukaya, Masakazu Kojima. Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems, Journal of Global Optimization, Vol. 24, No. 2, pp. 237-260, 2002.
• Masakazu Kojima, Levent Tuncel. Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems, Journal of Global Optimization, Vol. 24, pp. 333-348, 2002.
• Mituhiro Fukuda, Masakazu Kojima, Masayuki Shida. Lagrangian dual interior-point methods for semidefinite programs, SIAM Journal on Optimization, Vol. 12, No. 4, pp. 1007-1031, 2002.
• Sunyoung Kim, Masakazu Kojima. Second Order Cone Programming Relaxation of Nonconvex Quadratic Optimization Problems, Optimization Methods and Software, Vol. 15, No. 3-4, pp. 201-224, 2001.
• Masakazu Kojima, Akiko Takeda. Complexity Analysis of Conceptual Successive Convex Relaxation Methods for Nonconvex Sets, Mathematics of Operations Research, Vol. 26, No. 3, pp. 519-542, 2001.
• Mituhiro Fukuda, Masakazu Kojima. Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem, Computational Optimization and Applications, Vol. 19, No. 1, pp. 79-105, 2001.
• Levent Tuncel, Masakazu Kojima. Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets, SIAM Journal on Optimization, Vol. 10, No. 3, pp. 750-778, 2000.
• 松本敏浩, 小島政和, 信太正之. 穏やかな非凸計画問題の凹２次不等式条件１本付き凸計画問題への帰着, 電子情報通信学会和文論文誌, Vol. J83-A, No. 5, pp. 517-523, 2000.
• Masakazu Kojima, Levent Tuncel. Discretization and Localization in Successive Convex Relaxation for Nonconvex Quadratic Optimization Problems, Mathematical Programming, Vol. 89, No. 1, pp. 79-111, 2000.
• 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.
• Masakazu KOJIMA, Masayuki SHIDA, Susumu SHINDOH. A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton Search Direction, SIAM Journal on Optimization, Vol. 9, No. 2, pp. 444-465, 1999.
• Masakazu KOJIMA, Masayuki SHIDA, Susumu SHINDOH. A Note on Nesterov-Todd and Kojima-Shindoh-Hara Search Directions in Semidefinite Programming, Optimization Methods and Software, Vol. 11-12, pp. 47-52, 1999.
• Masakazu KOJIMA, Masayuki SHIDA, Susumu SHINDOH. Search Directions in the SDP and the Monotone SDLCP: Generalization and Inexact Computation, Mathematical Programming, Vol. 85, No. 1, pp. 51-80, 1999.
• M. Kojima, L. Tuncel. Monotonicity of Primal-Dual Interior-Point Algorithms for Semidefinite Programming Problems, Optimization Methods and Software, Vol. 10, No. 2, pp. 275-296, 1998.
• M. Kojima, M. Shida, S. Shindoh. Local Convergence of Predictor-Corrector Infeasible-Interior-Point Method for SDPs and SDLCPs, Mathematical Programming, Vol. 80, No. 2, pp. 129-160, 1998.
• M. Kojima, N. Megiddo, S. Mizuno. A Conjugate Direction Method for Approximating the Analytic Center of a Polytope, Journal of Inequalities and Applications, Vol. 2, No. 1, pp. 181-194, 1998.
• M. Shida, S. Shindoh, M. Kojima. Existence of Search Direction in Interior-Point Algorithms for the SDP and the Monotone SDLCP, SIAM Journal on Optimization, Vol. 8, No. 2, pp. 387-396, 1998.
• M. Kojima, S. Shindoh, S. Hara. Interior-Point Methods for the Monotone Linear Complementarity Problem with Symmetric Matrices, SIAM Journal on Optimization, Vol. 7, No. 1, pp. 86, 1997.
• T. Fujie, M. Kojima. Semidefinite Programming Relaxation for Nonconvex Quadratic Porgramming, Journal of Global Optimization, Vol. 10, No. 4, pp. 367-380, 1997.
• MASAKAZU KOJIMA. Reduction of Monotone Linear Complementarity Problems over Cones to Linear Programs over Cones, Acta Mathematica Vietnamica, Vol. 22, No. 1, pp. 147-157, 1997.
• MASAKAZU KOJIMA. Centers of Monotone Generalized Complementarity Problems, Mathematics of Operations Reserch, Vol. 22, No. 4, pp. 969-976, 1997.
• MASAKAZU KOJIMA. A Generalized Convexity and Uariateonal Inequalities for Quasiconvex Minimization, SIAM Journal on Optimization, Vol. 6, No. 1, pp. 212, 1996.
• MASAKAZU KOJIMA. Basic Lemmas in Polynomial-Time Infeasible-Interior-Point Methods for Linear Programs, Annals of Operations Reseach, Vol. 62, No. 1, pp. 1, 1996.
• MASAKAZU KOJIMA. Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming, SIAM Journal on Optimization, Vol. 5, No. 1, pp. 13-51, 1995.
• MASAKAZU KOJIMA. Global Convergence in Infeasible-Interior-Point Algorithms, Mathematical Programming, Vol. 65, No. 1, pp. 43-72, 1994.
• MASAKAZU KOJIMA. Large-Step Interior Point Algorithms for Linear Complementarity Problems, SIAM Jornal on Optimazation, Vol. 3, No. 2, pp. 398-412, 1993.
• MASAKAZU KOJIMA. A General Framework of Continuation Methods for Complementarity Problems, Mathematics of Operations Research, Vol. 18, No. 4, pp. 945-963, 1993.
• MASAKAZU KOJIMA. A primal-Dual Infeasible-Interior-Point Algorithm for Linear Programming, Mathematical Programming, Vol. 61, No. 3, pp. 263-280, 1993.
• MASAKAZU KOJIMA. A Primal-Dual Infeasible-Interior-Point Algorithm for Linear Programming, Mathematical Programming, Vol. 61, No. 3, pp. 263-280, 1993.
• MASAKAZU KOJIMA. On the Big Min the Affine Scaling Algorithm, Mathematical Programming Series B, Vol. 62, No. 1, pp. 85-93, 1993.
• MASAKAZU KOJIMA. A Little Theorem of the Big M in Interior Point Algorithms, Mathematical Programming, Vol. 59, No. 3, pp. 361-375, 1993.
• MASAKAZU KOJIMA. Theoretical Convergence of Large-Step Primal-Dual Interior Point Algorithms for Linear Programming, Mathematical Programming, Vol. 59, No. 1, pp. 1-22, 1993.
• MASAKAZU KOJIMA. An O(*L)Iteration Potential Reduction Algorithm for Linear Complementarity Problems, Mathematical Programming, Vol. 50, pp. 3, 1991.
• MASAKAZU KOJIMA. Homotopy Continuation Methods for Nonlinear Complementarity Problems, MAthematics of Operations Research, Vol. 16, pp. 4, 1991.
• MASAKAZU KOJIMA. A Polynomial-Time Algorithm for a Class of Linear Complementarity Problems, Mathematical Programming, Vol. 44, pp. 1, 1989.
• MASAKAZU KOJIMA. A Unified Approach to the Implementation of Several Restart Fixed Point Algorithms and a New Variable Dimension Algorithm, Mathematical Programming, Vol. 28, pp. 3, 1984.
• MASAKAZU KOJIMA. Computation of All Solutions to a System of Polynomial Equations, Mathematical Programming, Vol. 25, pp. 2, 1983.
• MASAKAZU KOJIMA. Variable Dimension Algorithms : Basic Theory, Interpretations and Extensions of Some Exisiting Methods, Mathematical Programming, Vol. 24, pp. 2, 1982.

著書

• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel primal-dual interior-point methods for semidefinite programs, Parallel Combinatorial Optimization (El-G. Talbi, Ed.), Chapter 9, John Wiley ＆ Sons, Inc, 2006.
• Katsuki Fujisawa, Masakazu Kojima, Akiko Takeda, Makoto Yamashita. High Performance Grid and Cluster Computing for Some Optimization Problems, Proceedings of SAINT 2004 Workshops, Proceedings of SAINT 2004 Workshops, pp. 612-615, 2004.
• Sunyoung Kim, Masakazu Kojima. CMPSm : A Continuation Method for Polynomial Systems (MATLAB version), Mathematical Software, Arjeh M Cohen, Xiao-Shan Gao and Nobuki Takakayama, Editors, World Scientific, Singapore, Mathematical Software, Arjeh M Cohen, Xiao-Shan Gao and Nobuki Takakayama, Editors, World Scientific, Singapore, pp. 285-295, 2002.
• Masakazu Kojima, Yang Dai, KatsukiFujisawa, Sunyoung Kim, Akiko Takeda. Parallel Implementation of Polyhedral Continuation Methods for Systems of Polynomial Equations, Mathematical Software, Arjeh M Cohen, Xiao-Shan Gao and Nobuki Takakayama, Editors, World Scientific, Singapore, Mathematical Software, Arjeh M Cohen, Xiao-Shan Gao and Nobuki Takakayama, Editors, World Scientific, Singapore, pp. 283-284, 2002.
• 小島政和, 土谷隆, 水野真治, 矢部博. 内点法, 朝倉書店, 朝倉書店, 2001.
• Akiko Takeda, Yang Dai, Mituhiro Fukuda, Masakazu Kojima. Towards Implemenations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, P. M. Pardalos, Editor, Kluwer Academic Press, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, P. M. Pardalos, Editor, Kluwer Academic Press, pp. 489-510, 2000.
• Akiko Takeda, Masakazu Kojima. Successive Convex Relaxation Apporach to Bilevel Quadratic Optimization Problems, Applications and Algorithms of Complementarity (M. C. Ferris, O. L. Mangasarian and J.-S. Pang, Editors), Kluwer Academic Publishers, Applications and Algorithms of Complementarity (M. C. Ferris, O. L. Mangasarian and J.-S. Pang, Editors), Kluwer Academic Publishers, pp. 317-340, 2000.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Numerical evaluation of the SDPA (semidefinite programming algorithm), High Performance Optimization (Frenk, H., Roos, K., Terlaky, T., Zhang, S. Eds.), Chapter 11, Springer, 2000.
• M. Kojima, N. Megiddo, T. Noma, A. Yoshise. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Springer-Verlag, Springer-Verlag, 1991.
• M. Kojima, S. Mizuno, A. Yoshise. A Primal-Dual Interior Point Algorithm for Linear Programming, Progress in Mathematical Programming, Progress in Mathematical Programming, 1989.
• 小島政和. 相補性と不動点 --- アルゴリズムによるアプローチ ---, 産業図書, 産業図書, 1981.
• 真壁肇, 小島政和, 牧野都治, 森村英典. オペレーションズ・リサーチ, 日本規格協会, 日本規格協会, 1980.
• MASAKAZU KOJIMA. Strongly Stable Stationary Solutions in Nonlinear Programs, Analysis and Computation of Fixed Points, Analysis and Computation of Fixed Points, 1980.

国際会議発表 (査読有り)

• Katsuki Fujisawa, Masakazu Kojima, Akiko Takeda, Makoto Yamashita. High Performance Grid and Cluster Computing for Some Optimization Problems, Proceedings of SAINT 2004 Work Shops, 2004.
• Akiko Takeda, Yang Dai, Mituhiro Fukuda, Masakazu Kojima. Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems (P. M. Pardalos, Ed.), Kluwer Academic Publishers (Dorchecht), pp. 489-510, 2000.

国際会議発表 (査読なし・不明)

• Makoto Yamashita, Masakazu Kojima. Ellipsoid-type Confidential Bounds on Semi-algebraic Sets via SDP Relaxation, Siam Conference on Optimization 2011, May 2011.
• Makoto Yamashita, Masakazu Kojima. Enclosing Ellipsoids of Semi-algebraic Sets, Nonlinear Optimization, Variational Inequalities and Equilibrium Problems, July 2010.
• Makoto Yamashita, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata, Katsuki Fujisawa, Kazuhiro Kobayashi, Maho Nakata. SDPA: Leading-edge software for SDP, Informs Annual Meeting 2008, Oct. 2008.
• Masakazu Kojima. Conversion methods for large scale SDPs to exploit their structured sparsity, The 4th Sino-Japanese Optimization Meeting, Aug. 2008.
• Kazuo Murota, Yoshihiro Kanno, Masakazu Kojima, Sadayoshi Kojima. A numerical algorithm for block-diagonal decomposition of matrix *-algebra, HPOPT 2008, June 2008.
• Masakazu Kojima, Sunyoung Kim, Hayato Waki. Elimination of free variables for solving linear optimization problems efficiently, SIAM Conference on Optimization, May 2008.
• Masakazu Kojima. Exploiting sparsity in polynomial optimization problems, Nonconvex Programming: Local and Global Approaches, Theory, Algorithms and Applications, Dec. 2007.
• Masakazu Kojima. Polyhedral homotopy methods vs semidefinite programming relaxations for problems involving polynomials, Workshop on Advances in Optimization, Apr. 2007.
• Masakazu Kojima. Polyhedral homotopy methods vs semidefinite programming relaxations for problems involving polynomials, Spring 2007 Workshop: Geometry of Mechanism Science, Mar. 2007.
• Masakazu Kojima. Sparsity in polynomial optimization, Workshop: Optimization and Control, Jan. 2007.
• Mituhiro Fukuda, Masakazu Kojima, Makoto Yamashita. Prospects on copositive programming, 19th International Symposium on Mathematical Programming, Aug. 2006.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata, Maho Nakata. Large-scale semidefinite programming from quantum chemistry, International Symposium on Mathematical Programming 2006, July 2006.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel Interior-Point Methods for Large Semi-Definite Programming, SIAM Conference on Parallel Processing for Scientific Computing 2006, Feb. 2006.
• Makoto Yamashita, Mituhiro Fukuda, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. SDPA(SemiDefinite Programming Algorithm) and its Parallel/Completion versions, Informs Annual Meeting 2005, Nov. 2005.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel Implementation for SemiDefinite Programming with Positive Definite Matrix Completion, International Conference on Continuous Optimization I, Aug. 2004.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Parallel Implementation of Interior-Point Methods for SemiDefinite Program, CORS/Informs Joint Meeting 2004, May 2004.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. Primal-Dual Interior-Point Methods of Semidefinite Programs, SIAM Conference on Parallel Processing for Scientific Computing 04, Feb. 2004.
• Kazuhide Nakata, Katsuki Fujisawa, Masakazu Kojima, Makoto Yamashita. Parallel Semidefinite Programming Algorithm Using Matrix Completion}, 18th International Symposium on mathematical programming, Aug. 2003.
• Masakazu Kojima, Kazuhide Nakata, Katsuki Fujisawa, Makoto Yamashita. Parallel implementation of primal-dual interior-point methods for semidefinite programs, 3rd McMaster Optimization Conference: Theory and Applications (MOPTA 03), July 2003.
• Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima. SDPARA (SemiDefinite Programming Algorithm PARAllel version), The Second Japanese-Sino Optimization Meeting, Sept. 2002.
• Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima}. Using the conjugate gradient method in the linear equation for interior-points methods of semidefinite programs, The Second Japanese-Sino Optimization Meeting(JSOM), Sept. 2002.
• 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.
• Kazuhide Nakata, Shao-Liang Zhang, Masakazu Kojima. Incomplete QR Preconditioner for Solving Large and Dense Linear Systems In Semidefinite Programming, 16th IMACS world congress, 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.
• Kazuhide Nakata, Shao-Liang Zhang, Masakazu Kojima. Krylov-subspace methods for large semidefinite programming, Optimization, Numerical Computation and Simulation in Applied Mathematics, 2000.
• Kazuhide Nakata, Shao-Liang Zhang, Masakazu Kojima. Preconditioned Conjugate Gradient Methods for Large Scale and Dense Linear Systems in Semidefinite Programming, INFORMS, Nov. 1999.
• Shao-Liang Zhang, Masakazu Kojima, Kazuhide Nakata. Incomplete orthogonalization preconditioner for solving large and dense linear systems which arise from semidefinite programming, The Sixth SIAM Conference on Optimization, May 1999.
• Masakazu Kojima, Katsuki Fujisawa, Kazuhide Nakata. Exploiting sparcity in primal-dual interior-point methods for semidefinite programming, International Symposium on Mathematical Programming, Aug. 1997.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata. Numerical Evaluation of the SDPA (SemiDefinite Programming Algorithm), International workshop on High Performance Optimization Technique, Aug. 1997.

国内会議発表 (査読なし・不明)

• 藤澤 克樹, 小島 政和, 中田 和秀, 福田 光浩, 山下 真, 中田 真秀. SDPA project and new features of SDPA 7.1.0, 算科学の基盤技術としての高速アルゴリズムとその周辺--RIMS研究集会, 数理解析研究所講究録, Vol. 1614, pp. 136-143, Oct. 2008.
• 小島政和. 多項式最適化問題に対する２乗多項式緩和, モデルベース統合化システム設計を支える数理 --- 数値・数式ハイブリッド計算・最適化の新展開 ---, Sept. 2008.
• 小島政和. 多項式最適化問題の半正定値計画緩和 --- 疎性の活用 ---, 最適化：モデリングとアルゴリズム, Mar. 2007.
• Mituhiro Fukuda, Masakazu Kojima, Makoto Yamashita. Computational prospects on copositive programming, Modeling and Optimization Theory, July 2006.
• 中田 和秀, 山下 真, 藤沢 克樹, 小島 政和. 半正定値計画に対する行列補完型主双対内点法の並列化, 日本オペレーションズ・リサーチ学会 ２００４年度春季研究発表会, Mar. 2004.
• 藤沢 克樹, 武田 朗子, 小島 政和, 中田 和秀. 広域分散コンピューティング環境における数理計画ソフトウェアSDPA, 情報処理学会研究報告. HPC, 情報処理学会研究報告. HPC, Vol. 83, pp. 31-36, May 2001.
• 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.
• 藤沢 克樹, 武田 朗子, 小島 政和, 中田 和秀. 半正定値計画問題に対するソフトウェアSDPAの広域並列計算システム, 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, 215-222, 2000.
• 藤沢 克樹, 武田 朗子, 小島 政和, 中田 和秀. 半正定値計画問題に対するソフトウェアSDPAの広域並列計算システム, 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. 138-145, 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.
• 張 紹良, 中田 和秀, 小島 政和. 半正定値計画問題に現れる密行列に対する前処理, 応用数学合同研究集会, Dec. 1999.
• 中田 和秀, 張 紹良, 小島 政和. 半正定値計画問題に適用する共役勾配法の前処理について, 日本応用数理学会 年会, July 1999.
• 中田 和秀, 張 紹良, 小島 政和. 半正定値計画問題での大規模線形方程式系に対する前処理付き共役勾配法, 京都大学数理解析研究所研究集会 「最適化のための連続と離散数理」, 数理解析研究所講究録, Vol. 1114, pp. 172-183, 1999.
• 藤沢 克樹, 小島 政和, 中田 和秀. 半正定値計画問題に対する内点法ソフトウェア, 京都大学数理解析研究所研究集会 「最適化のための連続と離散数理」, 数理解析研究所講究録, Vol. 1114, 149-159, 1999.
• 中田 和秀, 藤沢 克樹, 小島 政和. Semidefinite Programming with the Conjugate Gradient Method, 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１２」, 統計数理研究所共同研究レポート, Vol. 1113, pp. 224-247, 1998.

その他の論文・著書など

• Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Masakazu Kojima, Kazuhide Nakata, Maho Nakata, Makoto Yamashita. SDPA (SemiDefinite Programming Algorithm) User's Manual --- Version 7.0.5, Department of Mathematical and Computing Sciences Technical Report, No. 448, 2008.
• Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata, Makoto Yamashita. SDPA-C (SemiDefinite Programming Algorithm -- Completion method) User's Manual --- Version 6.10, Department of Mathematical and Computing Sciences Technical Report, No. 409, 2004.
• Satoshi Matsuyama, Satoshi Nakamura, Katsuki Fujisawa, Kazuhide Nakata, Masakazu Kojima. SDPA-M (SemiDefinite Programming Algorithm in MATLAB) User's Manual Version 1.00, Department of Mathematical and Computing Sciences Technical Report, No. 359, 2000.
• Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata. SDPA (Semidefinite Programming Algorithm) - User's Manual -, Department of Mathematical and Computing Sciences Technical Report, Tokyo Institute of Technology, No. 308, 1999.

学位論文

• Computational Methods for Solving the Nonlinear Complementarity Problem,  本文,  Doctor of Engineering,  慶應義塾大学大学院工学研究科,  1974/--/--, 

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