Publications

23-1. S. Kim, M. Kojima, "Strong duality of a conic optimization problem with a single hyperplane and two cone constraints",   Nov., 2021. Revised April22, 2023,   Slides of talk at Workshop on Continuous Optimization and Related Topics, Nov 27-28, 2021.  To appear in Optimization. 

22-1: S. Kim, M. Kojima and K. C. Toh, "Doubly Nonnegative Relaxations for Quadratic and Polynomial Optimization Problems with Binary and Box Constraints", Mathematical Programming, 193, 761-787 (2022).

21-1: S. Kim, M. Kojima and K. C. Toh,  A Newton-bracketing Method for a Simple Conic Optimization Problem, Optimization Methods and Software, 36:2-3, 371-388 .(2021). Software. Talk at the 5th ZIB-RIKEN-IMI-ISM MODAL Workshop.

20-2 :  S. Kim, M. Kojima and K.C. Toh, "A Geometric Analysis of a Class of Nonconvex Conic Programs for Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems", SIAM J. on Optimization, 30(2) 1251-1273 (2020). Talk at the 5th ZIB-RIKEN-IMI-ISM MODAL Workshop.

20-1 : S. Kim, M. Kojima and K.C. Toh, "Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures", Journal of Global Optimization, 77(3) 513-541 (2020).

19-2:  N. Arima, S. Kim, M. Kojima, and K.C. Toh, "Lagrangian-Conic Relaxations, Part II: Applications to Polynomial Optimization Problems", Pacific J. Optim, 15(3), 415-439 (2019). 

19-1: N. Ito, S. Kim, M. Kojima, A. Takeda and K.C. Toh,  "A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints'', ACM Transaction on Mathematical Software, 45(3) 34 (2019).  User Manual for BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints:  BBCPOP Homepage, 

18-2: N. Ito, S. Kim, M. Kojima, A. Takeda and K.C. Toh, " Equivalences and Differences in Conic Relaxations of Combinatorial Quadratic Optimization Problems", Journal of Global Optimization, 72(4) 619-653 (2018).

18-1: N. Arima, S. Kim, M. Kojima, and K.C. Toh, "Lagrangian-Conic Relaxations, Part I: A Unified Framework and Its Applications to Quadratic Optimization Problems", Pacific J. Optim. 14(1) 161-192 (2018). 

17-2: N. Arima, S. Kim, M. Kojima, and K.C. Toh, "A Robust Lagrangian-DNN Method for a Class of Quadratic Optimization Problems", Computational Optimization and Applications,  Vol 66(3) 453-479 (2017).

17-1: S. Kim and M. Kojima, "Binary Quadratic Optimization Problems That Are Difficult to Solve by Conic Relaxations", Discrete Optimization, Vol. 24 170-183 (2017).

16-2: S. Kim, M. Kojima, and K. C. Toh,"A Lagrangian-DNN Relaxation: A Fast Method for Computing Tight Lower Bounds for a Class of Quadratic Optimization Problems ", Mathematical Programming Vol. 156 161-187 (2016).

16-1: N. Arima, S. Kim and M. Kojima, "Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization", Journal of Optimization Theory and Applications Vol. 168 No. 3 884-900 (2016).

14-1: N. Arima, S. Kim and M. Kojima, "Simplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables ", Pacific Journal of Optimization Vol. 10 437-451 (2014).

13-3: N. Arima, S. Kim and Kojima, "A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming ", SIAM Journal of Optimization Vol. 23 2310-2340 (2013).

13-2: M. Kojima and M. Yamashita, "Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization", Mathematical Progmming Vol. 138 333-364 (2013).

13-1: S. Kim and M. Kojima, "A Continuation Method for Large-sized Sensor Network Localization Problems,", Pacific Journal of Optimization Vol. 9 117-136 (2013).

12-1: Kim, M. Kojima, H. Waki and M. Yamashita, "SFSDP: a Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problem". ACM Transactions on Mathematical Software Vo.38, 4 (2012).

11-1: S. Kim, M. Kojima, M. Mevissen and M. Yamashita, "Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion", Mathematical Programming Vol.129 33-68 (2011).

10-3: K. Murota, Y. Kanno, M. Kojima and S. 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.27 125-160 (2010). 

10-2: M. Mevissen and M. Kojima, "SDP Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems", Asia-Pacific Journal of Operational ResearchVol 27 (1) 15-38 (2010).

10-1: S. Kim and M. Kojima, "Solving polynomial least squares problems via semidefinite programming relaxations", Journal of Global Optimization VoL.46 (1) 1-23 (2010).

09-4: H. Waki, M. Muramatsu and M. Kojima, " Invariance under Affine Transformation in Semidefinite Programming Relaxation for Polynomial Optimization Problems ",  Pacific Journal of Optimization Vol 5 (2) 297-312 (2009).

09-3: S. Kim, M. Kojima and H. Waki, "Exploiting Sparsity in SDP Relaxation for Sensor Network Localization", SIAM Journal of Optimization Vol.20 (1) 192-215 (2009). 

09-2: S. Kim, M. Kojima and Ph. L Toint, " Recognizing Underlying Sparsity in Optimization ", Mathematical Programming Vol19 (2) 273-303 (2009). 

09-1: M. Kojima and M. Muramatsu, " A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones ", Computational Optimization and Applications Vol. 42 (1) 31-41 (2009). 

08-7: H. Waki, S. Kim, M. Kojima, M. Muramatsu and H. Sugimoto, "SparsePOP : a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems", ACM Transactions on Mathematical Software Vol 35 (2) 15 (2008). 

08-6: K. Kobayashi, S. Kim and M. Kojima, "Sparse Second Order Cone Programming Formulations for Convex Optimization Problems", Journal of the Operations Research Society of Japan Vol 51 (3) 241-264 (2008). 

08-5: K. Kobayashi, S. Kim and M. Kojima, "Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP and SOCP", Applied Mathematics and Optimization Vol 58 (1) 69-88 (2008).

08-4: K. Suzuki, N. Miyoshi and M. Kojima, "A Numerical Method for the Survival Probability of Diffusion Processes Using Semidefinite Programming" (in Japanese), Transactions of the Operations Research Society of Japan Vol.51 25-43 (2008).

08-3: M. Mevissen, M. Kojima, J. Nie and N. Takayama, "Solving partial differential equations via sparse SDP relaxations", Pacific Journal of Optimization Vol. 4 (2) 213 - 241 (2008).

08-2: C. Vo, M. Muramatsu and M. Kojima, " Equality Based Contraction of Semidefinite Programming Relaxations in Polynomial Optimization ", Journal of the Operations Research Society of Japan Vol. 51 (1) 111-125 (2008).

08-1: M. Kojima, "Efficient Evaluation of Polynomials and Their Partial Derivatives in Homotopy Continuation Methods", Journal of the Operations Research Society of Japan Vol. 51 (1) 29-54 (2008). 

07-3: M. Kojima and M. Muramatsu, "An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems over Symmetric Cones ", Mathematical Programming Vol. 110 (2) 315-336 (2007).

07-2: K. Kobayashi, K. Nakata and M. Kojima, "A Conversion of an SDP Having Free Variables into the Standard Form SDP" June 2005. Revised April 2006, Computational Optimization and Applications Vol. 36 289-307 (2007). 

07-1: T. Mizutani, A. Takeda and M. Kojima, " Dynamic Enumeration of All Mixed Cells ", Discrete and Computational Geometry Vol. 37 (3) 351-367 (2007). 

06-4: M. Yamashita, K. Fujisawa, M. Fukuda, M. Kojima and K. Nakata, "Parallel Primal-Dual Interior Point Methods for Semidefinite Programs", Parallel Combinatorial Optimization (El-Ghazali Talbi Editor), Wiley-Interscience, New Jersey, 2006, pp.211-238.

06-3: T. Gunji, S. Kim, K. Fujisawa and M. Kojima, "PHoMpara -- Parallel Implementation of the Polyhedral Homotopy Continuation Method ", Computing Vol. 77 (4) 387-411 (2006).

06-2: H. Waki, S. Kim, M. Kojima and M. Muramatsu, "Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity", SIAM Journal on Optimization Vol.17 (1) 218-242 (2006). 

06-1: K.Nakata, M.Yamashita, K.Fujisawa, M.Kojima, "A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix Completion". Parallel Computing Vol.32 24-43 (2006).

05-2: S. Kim, M. Kojima and H. Waki, "Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems", SIAM Journal on Optimization Vol. 15 (3) 697-719 (2005). 

05-1: M. Kojima, S. Kim and H. Waki, ``Sparsity in Sums of Squares of Polynomials'', Mathematical Programming Vol.103 (1) 45-62 (2005). 

04-5: K. Fujisawa, M. Kojima, A. Takeda and M. Yamashita, "Solving Large Scale Optimization Problems via Grid and Cluster Computing", Journal of Operations Research Society of Japan Vol.47 (4) 265-274 (2004).

04-4: S. Kim and M. Kojima, ``Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods'', Computing Vol. 73 (4) 329-348 (2004).

04-3: T. Gunji, S. Kim, M. Kojima, A. Takeda, K. Fujisawa and T. Mizutani, ``PHoM -- a Polyhedral Homotopy Continuation Method",Computing Vol.73 55-77 (2004).

04-2: C. Vo, A. Takeda and M. Kojima, "A Multilevel Parallelized Brancd and Bound Hybrid Algorithm for Quadratic Optimization", IPSJ Transactions on Advanced Computing SystemsVol.45, No.SIG 6(ACS 6) 186-196 (2004). 

04-1: K. Fujisawa, M. Kojima, A. Takeda and M. Yamashita, "High Performance Grid and Cluster Computing for Some Optimization Problems", Proceedings of SAINT 2004 Workshops, 612-615 (Tokyo, Japan, Jan. 26-30, 2004). 

03-7: M. Yamashita, K. Fujisawa and M. Kojima, ``SDPARA : SemiDefinite Programming Algorithm PARAllel Version'', Parallel Computing Vol.29 (8) 1053-1067 (2003).

03-6: S. Kim, M. Kojima and M. Yamashita, ``Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint'', Optimization Methods and Software Vol.18 (5) 535-541 (2003). 

03-5: S. Kim and M. Kojima, ``Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations,'' January 2002. Revised February 2003. Computational Optimization and Applications Vol.26 (2) 143-154 (2003).

03-4: M. Yamashita, K. Fujisawa and M. Kojima, ``Implementation and Evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0)'', Optimization Methods and Software Vol.18 (4) 491-505 (2003).

03-3: M. Kojima, S. Kim and H. Waki, ``A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones'', Journal of Operations Research Society of JapanVol.46 (2) 125-144 (2003).

03-2: 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 Vol.95 303-327 (2003).

03-1: Y. Dai, S. Kim and M. 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, 83-97 (2003). 

02-8: M. Kojima and L. Tuncel, ``Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems'',  Journal of Global Optimization Vol.24, 333-348 (2002).

02-7: M. Kojima and L. Tuncel, ``On the Finite Convergence of Successive SDP Relaxation Methods'' , European Journal of Operations Research Vol.143, No.2, 325-341 (2002).

02-6: A. Takeda, K. Fujisawa and Y. Fukaya and M. Kojima, ``Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems', Journal of Global Optimization, Vol.24, No.2, 237-260 (2002).

02-5: S. Kim and M. Kojima, ``CMPSm : A Continuation Method for Polynomial Systems (MATLAB version)'', Mathematical Software, ICMS2002 Beijing, China, August 17-19 (Arjeh M Cohen, Xiao-Shan Gao and Nobuki Takakayama, Editors), World Scientific, Singapore, 2002. 

02-4: Shao-Liang Zhang, K. Nakata and M. Kojima, ``Incomplete Orthogonalization Preconditioners for Solving Large and Dense Linear Systems Which Arise from Semidefinite Programming'', Applied Numerical Mathematics Vol 41, 235-245 (2002).

02-3: M. Fukuda, M. Kojima and M. Shida, ``Lagrangian Dual Interior-Point Methods for Semidefinite Programs'', SIAM Journal on Optimization Vol 12, No.4, 1007-1031 (2002).

02-2: Kim-Chuan Toh and M. Kojima, ``Solving some large scale semidenite programs via the conjugate residual method'' , SIAM Journal on Optimization Vol 12, No.3, 669-691 (2002).

02-1: A. Takeda, M. Kojima and K. Fujisawa ``Enumeration of All Solutions of a Combinatorial Linear Inequality System Arising from the Polyhedral Homotopy Continuation Method'' , Vol.45, No.1, 64-82 (2002).

01-5: M. Kojima and A. Takeda, ``Complexity Analysis of Conceptual Successive Convex Relaxation Methods for Nonconvex Sets'' , Mathematics of Operations Research Vol 26, No.3, 519-542 (2001).

01-4: M. Fukuda, M. Kojima, K. Murota and K. Nakata ``Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework'' , SIAM Journal on OptimizationVol 11, No.3, 647-674 (2001).

01-3: S. Kim and M. Kojima ``Second Order Cone Programming Relaxation of Nonconvex Quadratic Optimization Problems'', Optimization Methods and Software Vol .15, No.3-4 , 201-224 (2001).

01-2: M. Fukuda and M. Kojima, ``Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eignevalue Problem'' , Computational Optimization and Applications Vol.19, No.1, 79-105 (2001).

01-1: A. Takeda and M. 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, 2000, pp.317-340.

00-4: M. Kojima and L. Tuncel, ``Discretization and Localization in Successive Convex Relaxation for Nonconvex Quadratic Optimization Problems'';, Mathematical Programming Vol.89, No.1, 79-111 (2000).

00-3: A.Takeda, Y. Dai, M. Fukuda and M. 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, 2000, pp.489-510.

00-2: M. Kojima and L. Tuncel, ``Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets'' , SIAM Journal on Optimization Vol.10, No. 3, 750-778 (2000).

00-1: K. Fujisawa, M. Fukuda, M. Kojima and K. Nakata, ``Numerical Evaluation of SDPA (SemiDefinite Programming Algorithm)'', High Performance Optimization, H.Frenk, K. Roos, T. Terlaky and S. Zhang eds., Kluwer Academic Press, 2000, pp.267-301.

99-3: M. Kojima, M. Shida and S. Shindoh ``A Note on Nesterov-Todd and Kojima-Shindoh-Hara Search Directions in Semidefinite Programming'', Optimization Methods and Software Vol.11&12, 47-52 (December, 1999).

99-2: M. Kojima, M. Shida and S. 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, 444-465 (1999).

99-1: M. Kojima, M. Shida and S. Shindoh ``Search Directions in the SDP and the Monotone SDLCP: Generalization and Inexact Computation'', Mathematical Programming Vol.85, No.1, 51-80 (May, 1999)

98-4: M. Kojima and L. Tuncel, ``Monotonicity of Primal-Dual Interior-Point Algorithms for Semidefinite Programming Problems'', Optimization Methods and Software dedicated to the 65th birthday of Professor Masao Iri, Vol. 10, Number 2, 275-296 (December, 1998).

98-3: M. Shida, S. Shindoh and M. Kojima, ``Existence of Search Direction in Interior-Point Algorithms for the SDP and the Monotone SDLCP'' , SIAM Journal on Optimization, Vol.8, 387-396 (1998).

98-2: M. Kojima, N. Megiddo and S. Mizuno, ``A Conjugate Direction Method for Approximating the Analytic Center of a Polytope'', Journal of Inequalities and Applications, Vol. 2, 181-194 (1998).

98-1: M. Kojima, M. Shida and S. Shindoh, ``Local Convergence of Predictor-Corrector Infeasible-Interior-Point Method for SDPs and SDLCPs'',Mathematical Programming, Vol. 80,129-160 (1998).

97-5: M. Shida, S. Shindoh, M. Kojima, ``Centers of Monotone Generalized Complementarity Problems'',Mathematics of Operations Research, Vol. 22, 969-976 (1997).

97-4: M. Kojima, M. Shida and S. Shindoh, ``Reduction of Monotone Linear Complementarity Problems over Cones to Linear Programs over Cones'', Acta Mathematica Vietnamica, Vol. 22, 147-157 (1997).

97-3: K. Fujisawa, M. Kojima and K. Nakata, ``Exploiting Sparsity in Primal-Dual Interior-Point Methods for Semidefinite Programming'', Mathematical Programming, Series B, Vol. 79, 235-253 (1997).

97-2: T. Fujie and M. Kojima, ``Semidefinite Programming Relaxation for Nonconvex Quadratic Programming'', Journal of Global Optimization, Vol. 10, 367-380 (1997).

97-1: M. Kojima, S. Shindoh and S. Hara, ``Interior-Point Methods for the Monotone Linear Complementarity Problem in Symmetric Matrices'', SIAM J. Optimization, Vol. 7, 86-125 (1997).

96-2: M. Kojima, ``Basic Lemmas in Polynomial-Time Infeasible-Interior-Point Methods for Linear Programs,'' Annals of Operations Research, Vol. 62, 1-28 (1996).

96-1: P. T. Thach and M. Kojima, ``A Generalized Convexity and Variational Inequalities for Quasiconvex Minimization'', SIAM J. on Optimization, Vol. 6, 212-226 (1996).

95: S. Mizuno, M. Kojima and M. J. Todd, ``Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming'', SIAM Journal on Optimization, Vol. 5, 13-51 (1995).

94: M. Kojima, T. Noma and A. Yoshise, ``Global Convergence in Infeasible-Interior-Point Algorithms'', Mathematical Programming, Vol. 65, 43-72 (1994).

93-6: M. Kojima, Y. Kurita and S. Mizuno, ``Large-Step Interior Point Algorithms for Linear Complementarity Problems'' , SIAM Journal on Optimization, Vol. 3, 398-412 (1993).

93-5: M. Kojima, N. Megiddo and S. Mizuno``A General Framework of Continuation Methods for Complementarity Problems'', Mathematics of Operations Research, Vol. 18, 945-963 (1993).

93-4: T. Ishihara and M. Kojima, ``On the Big M in the Affine Scaling Algorithm'', Mathematical Programming, Series B, Vol. 62, 85-93 (1993).

93-3: M. Kojima, N. Megiddo and S. Mizuno, ``A Primal-Dual Infeasible-Interior-Point Algorithm for Linear Programming'', Mathematical Programming, Vol. 61, 263-280 (1993).

93-2: M. Kojima, S. Mizuno and A. Yoshise, ``A Little Theorem of the Big M in Interior Point Algorithms'', Mathematical Programming, Vol. 59 361-375 (1993).

93-1: M. Kojima, N. Megiddo and S. Mizuno, ``Theoretical Convergence of Large-Step Primal-Dual Interior Point Algorithms for Linear Programming'', Mathematical Programming, Vol. 59, 1-22 (1993).

92: M. Kojima, N. Megiddo and Y. Ye, ``An Interior Point Potential Reduction Algorithm for the Linear Complementarity Problem'' , Mathematical Programming, Series A, Vol. 54, 267-279 (1992).

91-5: M. Kojima, N. Megiddo, T. Noma and A. Yoshise, ``A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems: A Summary'', Operations Research Letters, Vol. 10, 247-254 (1991).

91-4:M. Kojima, N. Megiddo, T. Noma and A. Yoshise, ``A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems'', Lecture Notes in Computer Science, Vol. 538, Springer-Verlag, 1991.

91-3: M. Kojima, S. Mizuno and A. Yoshise, ``An O(\sqrt{n}) Iteration Potential Reduction Algorithm for Linear Complementarity Problems'', Mathematical Programming, Vol. 50, 331-342 (1991).

91-2: M. Kojima, N. Megiddo and T. Noma, ``Homotopy Continuation Methods for Nonlinear Complementarity Problems'', Mathematics of Operations Research, Vol. 16, 754-774 (1991).

91-1: M. Kojima and N. Megiddo, ``The Relation between the Path of Centers and Smale's Regularization of Linear Programming Problem'', Linear Algebra and Its Applications, Vol. 152, 135-139 (1991).

90-2: M. Kojima, S. Mizuno and T. Noma, ``Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems'', Mathematics of Operations Research, Vol.15, 662-675 (1990).

90-1: M. Kojima, S. Mizuno and A. Yoshise, ``Ellipsoids That Contain All the Solutions of a Positive Semi-Definite Linear Complementarity Problem'', Mathematical Programming, Vol. 48, 415-436 (1990).

89-3: M. Kojima, S. Mizuno and A. Yoshise, ``A Polynomial-Time Algorithm for a Class of Linear Complementarity Problems'', Mathematical Programming, Vol.44, 1-26 (1989).

89-2: M. Kojima, S. Mizuno and T, Noma, ``A New Continuation Method for Complementarity Problems with Uniform P-Functions'', Mathematical Programming, Vol.43, 107-113 (1989).

89-1: M. Kojima, S. Mizuno and A. Yoshise, ``A Primal-Dual Interior Point Algorithm for Linear Programming'', in: N. Megiddo, ed., Progress in Mathematical Programming: Interior Point and Related Methods (Springer-Verlag, New York) 29-47 (1989).

88: A. Tamura, H. Takehara, K. Fukuda, S. Fujishige and M. Kojima, ``A Dual Interior Primal Simplex Method for Linear Programming'', Journal of the Operations Research Society of Japan, Vol.31, 413-430 (1988).

87: Y. Ye and M. Kojima, ``Recovering Optimal Dual Solutions in Karmarkar's Polynomial Algorithm for Linear Programming'', Mathematical Programming, Vol.39, 305-317 (1987).

86-2: M. Kojima and S. Shindo, ``Extension of Newton and Quasi-Newton Methods to Systems ofPC^1 Equations'', Journal of Operations Society of Japan, Vol. 29, 352-374 (1986).

86-1: M. Kojima, ``Determining Basic Variables of Optimal Solutions in Karmarkar's New LP Algorithm,'' Algorithmica, Vol.1, 499-515 (1986).

85-2: M. Kojima, S. Oishi, Y. Sumi and K. Horiuchi``A PL Homotopy Continuation Method with the Use of an Odd Map for the Artificial Level'', Mathematical Programming, Vol.31, 235-244 (1985).

85-1: M. Kojima, A. Okada and S. Shindo, ``Strongly Stable Equilibrium Points of N-Person Noncooperative Games'', Mathematics of Operations Research, Vol.10, 650-663 (1985).

84-3: B. Yang and M. Kojima, ``Improving the Computational Efficiency of Fixed Point Algorithms'' (in Japanese), J. Operations Research Society of Japan, Vol. 27, 59-76 (1984).

84-2: M. Kojima and Y. Yamamoto, ``A Unified Approach to the Implementation of Several Restart Fixed Point Algorithms and a New Variable Dimension Algorithm'', Mathematical Programming, Vol.28, 288-328 (1984).

84-1: M. Kojima and R. Hirabayashi, ``Continuous Deformation of Nonlinear Programs'', Mathematical Programming Study, Vol.21, 150-198 (1984).

83: S. Mizuno and M. Kojima, ``Computation of All Solutions to a System of Polynomial Equations'' , Mathematical Programming, Vol.25, 131-157 (1983).

82: M. Kojima and Y. Yamamoto, ``Variable Dimension Algorithms: Basic Theory, Interpretations and Extensions of Some Existing Methods'', Mathematical Programming, Vol.24, 177-215 (1982).

81-2: M. Kojima and R. Saigal, ``On the Number of Solutions to a Class of Complementarity Problems'', Mathematical Programming, Vol.21, 190-203 (1981).

81-1: M. Kojima, ``An Introduction to Variable Dimension Algorithms for Solving Systems of Equations,'' in: E. L. Allgower, K.Glashoff and H.- O.Peitgen, ed., Numerical Solution of Nonlinear Equations (Springer-Verlag, Berlin) 200-237 (1981).

80-4: M. Kojima, ``Strongly Stable Stationary Solutions in Nonlinear Programs,'' in: S. M. Robinson ed., Analysis and Computation of Fixed Points (Academic Press, New York), 93-138 (1980).

80-3: M. Kojima, ``A Note on 'A New Algorithm for Computing Fixed Points' by van der Laan and Talman'', in: W. Forster, ed., Numerical Solution of Highly Nonlinear Problems (North-Holland, Amsterdam), 37-42 (1980).

80-2: M. Kojima and R. Saigal, ``On the Relationship between Conditions That Insure a PL Mapping Is a Homeomorphism'', Mathematics of Operations Research, Vol.5, 101-109 (1980).

80-1: M. Kojima and R. Saigal, ``A Property of Matrices with Positive Determinants'', Linear Algebra and Its Applications, Vol.30, 1-8 (1980).

79-4: M. Kojima and R. Saigal, ``On the Number of Solutions to a Class of Linear Complementarity Problems'', Mathematical Programming, Vol.17, 136-139 (1979).

79-3: M. Kojima, H. Nishino and A. Arima, ``A PL Homotopy for Finding All the Roots of a Polynomial'', Mathematical Programming, Vol.16, 37-62 (1979).

79-2: M. Kojima, ``A Complementarity Pivoting Approach to Parametric Nonlinear Programming,'' Mathematics of Operations Research, Vol.4, 464-477 (1979).

79-1: M. Kojima and r. Saigal, ``A Study of PC^1 Homeomorphisms of Subdivided Polyhedrons'', SIAM J. Math. Anal., Vol.10, 1299-1312 (1979).

78-3: M. Kojima, ``On the Homotopic Approach to Systems of Equations with Separable Mappings,'' Mathematical Programming Study, Vol.7, 170-184 (1978).

78-2: M. Kojima, ``A Modification of Todd's Triangulation J_3,'' Mathematical Programming, Vol.15 223-227 (1978).

78-1: M. Kojima, ``Studies on Piecewise-Linear Approximations of Piecewise C^1 Mappings in Fixed Points and Complementarity Theory,'' Mathematics of Operations Research, Vol.3, 17-36 (1978).

77: N. Megiddo and M. Kojima, ``On the Existence and Uniqueness of Solutions in Nonlinear Complementarity Theory'', Mathematical Programming, Vol.12, 110-130 (1977).

76-2: M. Kojiima, ``Vector Maximum Problems with Convexity,'' Pure and Applied Mathematika Sciences, Vol.3, 61-64 (1976).

76-1: M. Kojima, H. Nishino and T. Sekine, ``An Extension of Lemke's Method to the Piecewise Linear Complementarity Problem'', SIAM J. Appl. Math., Vol.31, 600-613 (1976).

75: M. Kojima, ``A Unification of the Existence Theorems of the Nonlinear Complementarity Problem,'' Mathematical Programming, Vol.9, 257-277 (1975).

74: M. Kojima, ``Computational Methods for Solving the Nonlinear Complementarity Problem,'' Keio Engineering Reports, Vol.27, 1-41 (1974).

72: M. Kojima, ``Duality between Objects and Constraints in Vector Optimum Problems,'' J. Operations Research Soc. of Japan, Vol.15, 53-62 (1972).

71: M. Kojima, ``Vector Maximum Problems,'' Keio Engineering Reports, Vol.24, 47-64 (1971).