**Refereed Publications (Last Update February 2016)**

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16-2: S. Kim, M. Kojima and K. 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 Research* Vol 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). MATLAB software
package SFSDP.

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 __P__olyhedral __Ho__motopy Continuation __M__ethod
", *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 __P__olyhedral __Ho__motopy Continuation __M__ethod",*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 Systems* Vol.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 : __S__emi__D__efinite__
P__rogramming __A__lgorithm PA__RA__llel 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 Japan* Vol.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).
Solution Information on Some Polynomial Systems.

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. Gzipped tarred files of the entire CMPSm system.

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'' ,
*Journal of the Operations Research Society of Japan* 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 Optimization* Vol 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 V*ol.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).

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