# zbMATH — the first resource for mathematics

## Kojima, Masakazu

Compute Distance To:
 Author ID: kojima.masakazu Published as: Kojima, M.; Kojima, Masakazu External Links: MGP
 Documents Indexed: 142 Publications since 1972, including 1 Book
all top 5

#### Co-Authors

 15 single-authored 33 Kim, Sunyoung 14 Mizuno, Shinji 13 Fujisawa, Katsuki 12 Takeda, Akiko 10 Megiddo, Nimrod 10 Nakata, Kazuhide 10 Shindoh, Susumu 9 Fukuda, Mituhiro 9 Shida, Masayuki 8 Yoshise, Akiko 7 Waki, Hayato 6 Arima, Naohiko 6 Noma, Toshihito 6 Yamashita, Makoto 5 Muramatsu, Masakazu 5 Murota, Kazuo 5 Toh, Kim-Chuan 5 Tunçel, Levent 4 Saigal, Romesh 4 Toh, Kimchuan 3 Dai, Yang 3 Kobayashi, Kazuhiro 3 Mevissen, Martin 2 Fujie, Tetsuya 2 Hara, Shinji 2 Ito, Naoki 2 Kojima, Sadayoshi 2 Mizutani, Tomohiko 2 Nishino, Hisakazu 2 Yamamoto, Yoshitsugu 2 Ye, Yinyu 2 Zhang, Shao-Liang 1 Arima, Naohiko 1 Burer, Samuel 1 Fujishige, Satoru 1 Fukaya, Yusuke 1 Fukuda, Komei 1 Gunji, Takayuki 1 Hirabayashi, Ryuichi 1 Horiuchi, Kazuo 1 Ishihara, Tohru 1 Kanno, Yoshihiro 1 Kurita, Yoshifumi 1 Matsumoto, Toshihiro 1 Nie, Jiawang 1 Oishi, Shin’ichi 1 Okada, Akira 1 Sekine, Tomoharu 1 Sumi, Yoichi 1 Takayama, Nobuki 1 Takehara, Hitoshi 1 Tamura, Akihisa 1 Thach, Phan Thien 1 Todd, Michael J. 1 Toint, Philippe L. 1 Vo, Cong 1 Yang, Bing
all top 5

#### Serials

 21 Mathematical Programming. Series A. Series B 15 SIAM Journal on Optimization 11 Mathematical Programming 10 Journal of the Operations Research Society of Japan 10 RIMS Kokyuroku 9 Mathematics of Operations Research 6 Journal of Global Optimization 6 Computational Optimization and Applications 6 Pacific Journal of Optimization 5 Optimization Methods & Software 2 ACM Transactions on Mathematical Software 2 Mathematical Programming Study 2 Linear Algebra and its Applications 1 Acta Mathematica Vietnamica 1 Applied Mathematics and Optimization 1 Computing 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Operations Research Letters 1 Applied Numerical Mathematics 1 Algorithmica 1 Discrete & Computational Geometry 1 Asia-Pacific Journal of Operational Research 1 Annals of Operations Research 1 Japan Journal of Industrial and Applied Mathematics 1 European Journal of Operational Research 1 SIAM Journal on Applied Mathematics 1 Journal of Inequalities and Applications 1 Discrete Optimization 1 Lecture Notes in Computer Science
all top 5

#### Fields

 119 Operations research, mathematical programming (90-XX) 47 Numerical analysis (65-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Computer science (68-XX) 4 Real functions (26-XX) 4 General topology (54-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Convex and discrete geometry (52-XX) 2 Algebraic topology (55-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX)

#### Citations contained in zbMATH

114 Publications have been cited 2,132 times in 1,339 Documents Cited by Year
A unified approach to interior point algorithms for linear complementarity problems: A summary. Zbl 0745.90069
Kojima, Masakazu; Megiddo, Nimrod; Noma, Toshihito; Yoshise, Akiko
1991
Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. Zbl 0872.90098
Kojima, Masakazu; Shindoh, Susumu; Hara, Shinji
1997
A polynomial-time algorithm for a class of linear complementarity problems. Zbl 0676.90087
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1989
A primal-dual interior point algorithm for linear programming. Zbl 0708.90049
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1989
A primal-dual infeasible-interior-point algorithm for linear programming. Zbl 0808.90093
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity. Zbl 1109.65058
Waki, Hayato; Kim, Sunyoung; Kojima, Masakazu; Muramatsu, Masakazu
2006
An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems. Zbl 0738.90077
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1991
Extension of Newton and quasi-Newton methods to systems of $$PC^ 1$$ equations. Zbl 0611.65032
Kojima, Masakazu; Shindo, Susumu
1986
Exploiting sparsity in semidefinite programming via matrix completion. I: General framework. Zbl 1010.90053
Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo; Nakata, Kazuhide
2000
Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs. Zbl 0897.90183
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1998
A unified approach to interior point algorithms for linear complementary problems. Zbl 0766.90077
Kojima, Masakazu (ed.); Megiddo, Nimrod (ed.); Noma, Toshihito (ed.); Yoshise, Akiko (ed.)
1991
Homotopy continuation methods for nonlinear complementarity problems. Zbl 0744.90087
Kojima, Masakazu; Megiddo, Nimrod; Noma, Toshihito
1991
Implementation and evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0). Zbl 1106.90366
Yamashita, Makoto; Fujisawa, Katsuki; Kojima, Masakazu
2003
Semidefinite programming relaxation for nonconvex quadratic programs. Zbl 0881.90101
Fujie, Tetsuya; Kojima, Masakazu
1997
Sparsity in sums of squares of polynomials. Zbl 1079.90092
Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato
2005
An interior point potential reduction algorithm for the linear complementarity problem. Zbl 0764.90083
Kojima, Masakazu; Megiddo, Nimrod; Ye, Yinyu
1992
Recovering optimal dual solutions in Karmarkar’s polynomial algorithm for linear programming. Zbl 0639.90062
Ye, Yinyu; Kojima, Masakazu
1987
Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results. Zbl 1030.90081
Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo
2003
Second order cone programming relaxation of nonconvex quadratic optimization problems. Zbl 1109.90327
Kim, Sunyoung; Kojima, Masakazu
2001
Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. Zbl 0979.65051
Fukuda, Mituhiro; Kojima, Masakazu
2001
Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076
Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J.
1995
A unification of the existence theorems of the nonlinear complementarity problem. Zbl 0347.90039
Kojima, Masakazu
1975
On the calculation of Stokes’ flow past porous particles. Zbl 0484.76049
Higdon, J. J. L.; Kojima, M.
1981
Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems. Zbl 0719.90085
Kojima, Masakazu; Mizuno, Shinji; Noma, Toshihito
1990
A new continuation method for complementarity problems with uniform P- functions. Zbl 0673.90084
Kojima, Masakazu; Mizuno, Shinji; Noma, Toshihito
1989
Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Zbl 1043.90060
Kim, Sunyoung; Kojima, Masakazu
2003
Cones of matrices and successive convex relaxations of nonconvex sets. Zbl 0966.90062
Kojima, Masakazu; Tunçel, Levent
2000
Continuous deformation of nonlinear programs. Zbl 0569.90074
Kojima, Masakazu; Hirabayashi, Ryuichi
1984
A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. Zbl 1342.90123
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2016
Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods. Zbl 0509.90070
Kojima, Masakazu; Yamamoto, Yoshitsugu
1982
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. Zbl 0887.90156
Fujisawa, Katsuki; Kojima, Masakazu; Nakata, Kazuhide
1997
On the existence and uniqueness of solutions in nonlinear complementarity theory. Zbl 0363.90102
Megiddo, Nimrod; Kojima, Masakazu
1977
Generalized Lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems. Zbl 1114.90085
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato
2005
PHoM – a polyhedral homotopy continuation method for polynomial systems. Zbl 1061.65041
Gunji, Takayuki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Fujisawa, Katsuki; Mizutani, Tomohiko
2004
Global convergence in infeasible-interior-point algorithms. Zbl 0820.90106
Kojima, Masakazu; Noma, Toshihito; Yoshise, Akiko
1994
Strongly stable stationary solutions in nonlinear programs. Zbl 0478.90062
Kojima, Masakazu
1980
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones. Zbl 1153.90545
Kojima, Masakazu; Muramatsu, Masakazu
2009
Solving some large scale semidefinite programs via the conjugate residual method. Zbl 1008.90043
Toh, Kim-Chuan; Kojima, Masakazu
2002
A predictor-corrector interior-point algorithm for the semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction. Zbl 0997.90086
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
On the number of solutions to a class of linear complementarity problems. Zbl 0413.90073
Kojima, M.; Saigal, Romesh
1979
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion. Zbl 1229.90116
Kim, Sunyoung; Kojima, Masakazu; Mevissen, Martin; Yamashita, Makoto
2011
An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones. Zbl 1210.90159
Kojima, Masakazu; Muramatsu, Masakazu
2007
Numerical evaluation of SDPA (semidefinite programming algorithm). Zbl 0952.90047
Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Nakata, Kazuhide
2000
Existence and uniqueness of search directions in interior-point algorithms for the SDP and the monotone SDLCP. Zbl 0913.90252
Shida, Masayuki; Shindoh, Susumu; Kojima, Masakazu
1998
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with application to semidefinite programming. Zbl 1204.65068
Murota, Kazuo; Kanno, Yoshihiro; Kojima, Masakazu; Kojima, Sadayoshi
2010
A quadratically constrained quadratic optimization model for completely positive cone programming. Zbl 1304.90152
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2013
Exploiting sparsity in SDP relaxation for sensor network localization. Zbl 1190.65096
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato
2009
Theoretical convergence of large-step primal-dual interior point algorithms for linear programming. Zbl 0780.90063
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
Dynamic enumeration of all mixed cells. Zbl 1113.65055
Mizutani, Tomohiko; Takeda, Akiko; Kojima, Masakazu
2007
Simplified copositive and Lagrangian relaxations for linearly constrained quadratic optimization problems in continuous and binary variables. Zbl 1327.90161
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2014
A general framework of continuation methods for complementarity problems. Zbl 0801.90108
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. Zbl 0539.65036
Kojima, Masakazu; Yamamoto, Yoshitsugu
1984
Algorithm 920: SFSDP: a sparse version of full semidefinite programming relaxation for sensor network localization problems. Zbl 1365.65163
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato; Yamashita, Makato
2012
Large-step interior point algorithms for linear complementarity problems. Zbl 0781.90085
Kojima, Masakazu; Kurita, Yoshifumi; Mizuno, Shinji
1993
Strongly stable equilibrium points of n-person noncooperative games. Zbl 0581.90098
Kojima, M.; Okada, A.; Shindoh, S.
1985
On the relationship between conditions that insure a PL mapping is a homeomorphism. Zbl 0441.57018
Kojima, M.; Saigal, Romesh
1980
Studies on piecewise-linear approximations of piecewise-$$C^1$$ mappings in fixed points and complementarity theory. Zbl 0396.41012
Kojima, Masakazu
1978
A general framework for convex relaxation of polynomial optimization problems over cones. Zbl 1049.90052
Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato
2003
A PL homotopy for finding all the roots of a polynomial. Zbl 0395.65016
Kojima, Masakazu; Nishino, Hisakazu; Arima, Naohiko
1979
Computational methods for solving the nonlinear complementarity problem. Zbl 0406.90071
Kojima, Masakazu
1974
Correlative sparsity in primal-dual interior-point methods for LP, SDP, and SOCP. Zbl 1191.90032
Kobayashi, Kazuhiro; Kim, Sunyoung; Kojima, Masakazu
2008
Linear algebra for semidefinite programming. Zbl 0971.90089
Kojima, Masakazu; Kojima, Sadayoshi; Hara, Shinji
1997
Computation of all solutions to a system of polynomial equations. Zbl 0517.90062
Kojima, Masakazu; Mizuno, Shinji
1983
Recognizing underlying sparsity in optimization. Zbl 1163.90026
Kim, Sunyoung; Kojima, Masakazu; Toint, Philippe
2009
Search directions in the SDP and the monotone SDLCP: Generalization and inexact computation. Zbl 0948.90115
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
Basic lemmas in polynomial-time infeasible-interior-point methods for linear programs. Zbl 0848.90084
Kojima, Masakazu
1996
A little theorem of the big $${\mathcal M}$$ in interior point algorithms. Zbl 0793.90083
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1993
Determining basic variables of optimal solutions in Karmarkar’s new LP algorithm. Zbl 0661.90057
Kojima, Masakazu
1986
On the homotopic approach to systems of equations with separable mappings. Zbl 0396.65024
Kojima, Masakazu
1978
Extension of completely positive cone relaxation to moment cone relaxation for polynomial optimization. Zbl 1336.90068
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2016
Burer, Samuel; Kim, Sunyoung; Kojima, Masakazu
2014
Numerical stability of path tracing in polyhedral homotopy continuation methods. Zbl 1061.65042
Kim, S.; Kojima, M.
2004
Second order cone programming relaxation of a positive semidefinite constraint. Zbl 1142.90466
Kim, Sunyoung; Kojima, Masakazu; Yamashita, Makoto
2003
Lagrangian dual interior-point methods for semidefinite programs. Zbl 1035.90054
Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki
2002
Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization. Zbl 1060.90058
Kojima, Masakazu; Tunçel, Levent
2000
A robust Lagrangian-DNN method for a class of quadratic optimization problems. Zbl 1366.90152
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2017
Computing all nonsingular solutions of cyclic-$$n$$ polynomial using polyhedral homotopy continuation methods. Zbl 1018.65068
Dai, Yang; Kim, Sunyoung; Kojima, Masakazu
2003
Optimal numbers of two kinds of kanbans in a JIT production system. Zbl 0917.90173
Ohno, K.; Nakashima, K.; Kojima, M.
1995
A modification of Todd’s triangulation $$J_3$$. Zbl 0385.65029
Kojima, Masakazu
1978
Solving partial differential equations via sparse SDP relaxations. Zbl 1161.90458
Mevissen, Martin; Kojima, Masakazu; Nie, Jiawang; Takayama, Nobuki
2008
Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method. Zbl 1031.65074
Takeda, Akiko; Kojima, Masakazu; Fujisawa, Katsuki
2002
On the finite convergence of successive SDP relaxation methods. Zbl 1058.90048
Kojima, Masakazu; Tuncel, Levent
2002
Centers of monotone generalized complementarity problems. Zbl 0892.90175
Shida, Masayuki; Shindoh, Susumu; Kojima, Masakazu
1997
An introduction to variable dimension algorithms for solving systems of equations. Zbl 0471.65030
Kojima, Masakazu
1981
On the number of solutions to a class of complementarity problems. Zbl 0461.90066
Kojima, M.; Saigal, Romesh
1981
Algorithm 996: BBCPOP: a sparse doubly nonnegative relaxation of polynomial optimization problems with binary, box, and complementarity constraints. Zbl 07193383
Ito, Naoki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Toh, Kim-Chuan
2019
Sparse second order cone programming formulations for convex optimization problems. Zbl 1152.90560
Kobayashi, Kazuhiro; Kim, Sunyoung; Kojima, Masakazu
2008
A conversion of an SDP having free variables into the standard form SDP. Zbl 1146.90492
Kobayashi, Kazuhiro; Nakata, Kazuhide; Kojima, Masakazu
2007
Some fundamental properties of successive convex relaxation methods on LCP and related problems. Zbl 1046.90062
Kojima, Masakazu; Tunçel, Levent
2002
CMPSM: A continuation method for polynomial systems (MATLAB version). Zbl 1011.68191
Kim, Sunyoung; Kojima, Masakazu
2002
Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems. Zbl 0966.65054
Takeda, Akiko; Dai, Yang; Fukuda, Mituhiro; Kojima, Masakazu
2000
A note on the Nesterov-Todd and the Kojima-Shindoh-Hara search directions in semidefinite programming. Zbl 0957.90104
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
Reduction of monotone linear complementarity problems over cones to linear programs over cones. Zbl 0903.90165
Kojima, M.; Shida, M.; Shindoh, S.
1997
A generalized convexity and variational inequality for quasi-convex minimization. Zbl 0841.49019
Thach, Phan Thien; Kojima, Masakazu
1996
A dual interior primal simplex method for linear programming. Zbl 0658.90062
Tamura, Akihisa; Takehara, Hitoshi; Fukuda, Komei; Fujishige, Satoru; Kojima, Masakazu
1988
A complementary pivoting approach to parametric nonlinear programming. Zbl 0428.49028
Kojima, Masakazu
1979
An extension of Lemke’s method to the piecewise linear complementarity problem. Zbl 0355.90060
Kojima, Masakazu; Nishino, Hisakazu; Sekine, Tomoharu
1976
A geometrical analysis on convex conic reformulations of quadratic and polynomial optimization problems. Zbl 07202484
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2020
Binary quadratic optimization problems that are difficult to solve by conic relaxations. Zbl 1387.90175
Kim, Sunyoung; Kojima, Masakazu
2017
Exploiting sparsity in SDP relaxation of polynomial optimization problems. Zbl 1334.90107
Kim, Sunyoung; Kojima, Masakazu
2012
A geometrical analysis on convex conic reformulations of quadratic and polynomial optimization problems. Zbl 07202484
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2020
Algorithm 996: BBCPOP: a sparse doubly nonnegative relaxation of polynomial optimization problems with binary, box, and complementarity constraints. Zbl 07193383
Ito, Naoki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Toh, Kim-Chuan
2019
A robust Lagrangian-DNN method for a class of quadratic optimization problems. Zbl 1366.90152
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2017
Binary quadratic optimization problems that are difficult to solve by conic relaxations. Zbl 1387.90175
Kim, Sunyoung; Kojima, Masakazu
2017
A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. Zbl 1342.90123
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan
2016
Extension of completely positive cone relaxation to moment cone relaxation for polynomial optimization. Zbl 1336.90068
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2016
Simplified copositive and Lagrangian relaxations for linearly constrained quadratic optimization problems in continuous and binary variables. Zbl 1327.90161
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2014
Burer, Samuel; Kim, Sunyoung; Kojima, Masakazu
2014
A quadratically constrained quadratic optimization model for completely positive cone programming. Zbl 1304.90152
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu
2013
Algorithm 920: SFSDP: a sparse version of full semidefinite programming relaxation for sensor network localization problems. Zbl 1365.65163
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato; Yamashita, Makato
2012
Exploiting sparsity in SDP relaxation of polynomial optimization problems. Zbl 1334.90107
Kim, Sunyoung; Kojima, Masakazu
2012
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion. Zbl 1229.90116
Kim, Sunyoung; Kojima, Masakazu; Mevissen, Martin; Yamashita, Makoto
2011
A numerical algorithm for block-diagonal decomposition of matrix $$*$$-algebras with application to semidefinite programming. Zbl 1204.65068
Murota, Kazuo; Kanno, Yoshihiro; Kojima, Masakazu; Kojima, Sadayoshi
2010
Solving polynomial least squares problems via semidefinite programming relaxations. Zbl 1181.90224
Kim, Sunyoung; Kojima, Masakazu
2010
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones. Zbl 1153.90545
Kojima, Masakazu; Muramatsu, Masakazu
2009
Exploiting sparsity in SDP relaxation for sensor network localization. Zbl 1190.65096
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato
2009
Recognizing underlying sparsity in optimization. Zbl 1163.90026
Kim, Sunyoung; Kojima, Masakazu; Toint, Philippe
2009
Invariance under affine transformation in semidefinite programming relaxation for polynomial optimization problems. Zbl 1192.90138
Waki, Hayato; Muramatsu, Masakazu; Kojima, Masakazu
2009
Correlative sparsity in primal-dual interior-point methods for LP, SDP, and SOCP. Zbl 1191.90032
Kobayashi, Kazuhiro; Kim, Sunyoung; Kojima, Masakazu
2008
Solving partial differential equations via sparse SDP relaxations. Zbl 1161.90458
Mevissen, Martin; Kojima, Masakazu; Nie, Jiawang; Takayama, Nobuki
2008
Sparse second order cone programming formulations for convex optimization problems. Zbl 1152.90560
Kobayashi, Kazuhiro; Kim, Sunyoung; Kojima, Masakazu
2008
Equality based contraction of semidefinite programming relaxations in polynomial optimization. Zbl 1176.90581
Vo, Cong; Muramatsu, Masakazu; Kojima, Masakazu
2008
Efficient evaluation of polynomials and their partial derivatives in homotopy continuation methods. Zbl 1173.90513
Kojima, Masakazu
2008
An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones. Zbl 1210.90159
Kojima, Masakazu; Muramatsu, Masakazu
2007
Dynamic enumeration of all mixed cells. Zbl 1113.65055
Mizutani, Tomohiko; Takeda, Akiko; Kojima, Masakazu
2007
A conversion of an SDP having free variables into the standard form SDP. Zbl 1146.90492
Kobayashi, Kazuhiro; Nakata, Kazuhide; Kojima, Masakazu
2007
Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity. Zbl 1109.65058
Waki, Hayato; Kim, Sunyoung; Kojima, Masakazu; Muramatsu, Masakazu
2006
Sparsity in sums of squares of polynomials. Zbl 1079.90092
Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato
2005
Generalized Lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems. Zbl 1114.90085
Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato
2005
PHoM – a polyhedral homotopy continuation method for polynomial systems. Zbl 1061.65041
Gunji, Takayuki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Fujisawa, Katsuki; Mizutani, Tomohiko
2004
Numerical stability of path tracing in polyhedral homotopy continuation methods. Zbl 1061.65042
Kim, S.; Kojima, M.
2004
Implementation and evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0). Zbl 1106.90366
Yamashita, Makoto; Fujisawa, Katsuki; Kojima, Masakazu
2003
Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results. Zbl 1030.90081
Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo
2003
Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Zbl 1043.90060
Kim, Sunyoung; Kojima, Masakazu
2003
A general framework for convex relaxation of polynomial optimization problems over cones. Zbl 1049.90052
Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato
2003
Second order cone programming relaxation of a positive semidefinite constraint. Zbl 1142.90466
Kim, Sunyoung; Kojima, Masakazu; Yamashita, Makoto
2003
Computing all nonsingular solutions of cyclic-$$n$$ polynomial using polyhedral homotopy continuation methods. Zbl 1018.65068
Dai, Yang; Kim, Sunyoung; Kojima, Masakazu
2003
Solving some large scale semidefinite programs via the conjugate residual method. Zbl 1008.90043
Toh, Kim-Chuan; Kojima, Masakazu
2002
Lagrangian dual interior-point methods for semidefinite programs. Zbl 1035.90054
Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki
2002
Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method. Zbl 1031.65074
Takeda, Akiko; Kojima, Masakazu; Fujisawa, Katsuki
2002
On the finite convergence of successive SDP relaxation methods. Zbl 1058.90048
Kojima, Masakazu; Tuncel, Levent
2002
Some fundamental properties of successive convex relaxation methods on LCP and related problems. Zbl 1046.90062
Kojima, Masakazu; Tunçel, Levent
2002
CMPSM: A continuation method for polynomial systems (MATLAB version). Zbl 1011.68191
Kim, Sunyoung; Kojima, Masakazu
2002
Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming. Zbl 0994.65050
Zhang, Shao-Liang; Nakata, Kazuhide; Kojima, Masakazu
2002
Second order cone programming relaxation of nonconvex quadratic optimization problems. Zbl 1109.90327
Kim, Sunyoung; Kojima, Masakazu
2001
Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem. Zbl 0979.65051
Fukuda, Mituhiro; Kojima, Masakazu
2001
Complexity analysis of successive convex relaxation methods for nonconvex sets. Zbl 1073.90580
Kojima, Masakazu; Takeda, Akiko
2001
Exploiting sparsity in semidefinite programming via matrix completion. I: General framework. Zbl 1010.90053
Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo; Nakata, Kazuhide
2000
Cones of matrices and successive convex relaxations of nonconvex sets. Zbl 0966.90062
Kojima, Masakazu; Tunçel, Levent
2000
Numerical evaluation of SDPA (semidefinite programming algorithm). Zbl 0952.90047
Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Nakata, Kazuhide
2000
Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization. Zbl 1060.90058
Kojima, Masakazu; Tunçel, Levent
2000
Towards implementations of successive convex relaxation methods for nonconvex quadratic optimization problems. Zbl 0966.65054
Takeda, Akiko; Dai, Yang; Fukuda, Mituhiro; Kojima, Masakazu
2000
A predictor-corrector interior-point algorithm for the semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction. Zbl 0997.90086
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
Search directions in the SDP and the monotone SDLCP: Generalization and inexact computation. Zbl 0948.90115
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
A note on the Nesterov-Todd and the Kojima-Shindoh-Hara search directions in semidefinite programming. Zbl 0957.90104
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1999
Moderate nonconvexity = convexity + quadratic concavity. Zbl 0957.90508
Kojima, Masakazu; Matsumoto, Toshihiro; Shida, Masayuki
1999
The interior-point method software SDPA (semidefinite programming algorithm) for semidefinite programming problems. Zbl 0957.90505
Fujisawa, Katsuki; Kojima, Masakazu; Nakata, Kazuhide
1999
Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs. Zbl 0897.90183
Kojima, Masakazu; Shida, Masayuki; Shindoh, Susumu
1998
Existence and uniqueness of search directions in interior-point algorithms for the SDP and the monotone SDLCP. Zbl 0913.90252
Shida, Masayuki; Shindoh, Susumu; Kojima, Masakazu
1998
Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. Zbl 0872.90098
Kojima, Masakazu; Shindoh, Susumu; Hara, Shinji
1997
Semidefinite programming relaxation for nonconvex quadratic programs. Zbl 0881.90101
Fujie, Tetsuya; Kojima, Masakazu
1997
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. Zbl 0887.90156
Fujisawa, Katsuki; Kojima, Masakazu; Nakata, Kazuhide
1997
Linear algebra for semidefinite programming. Zbl 0971.90089
Kojima, Masakazu; Kojima, Sadayoshi; Hara, Shinji
1997
Centers of monotone generalized complementarity problems. Zbl 0892.90175
Shida, Masayuki; Shindoh, Susumu; Kojima, Masakazu
1997
Reduction of monotone linear complementarity problems over cones to linear programs over cones. Zbl 0903.90165
Kojima, M.; Shida, M.; Shindoh, S.
1997
Basic lemmas in polynomial-time infeasible-interior-point methods for linear programs. Zbl 0848.90084
Kojima, Masakazu
1996
A generalized convexity and variational inequality for quasi-convex minimization. Zbl 0841.49019
Thach, Phan Thien; Kojima, Masakazu
1996
Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076
Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J.
1995
Optimal numbers of two kinds of kanbans in a JIT production system. Zbl 0917.90173
Ohno, K.; Nakashima, K.; Kojima, M.
1995
Global convergence in infeasible-interior-point algorithms. Zbl 0820.90106
Kojima, Masakazu; Noma, Toshihito; Yoshise, Akiko
1994
A primal-dual infeasible-interior-point algorithm for linear programming. Zbl 0808.90093
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
Theoretical convergence of large-step primal-dual interior point algorithms for linear programming. Zbl 0780.90063
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
A general framework of continuation methods for complementarity problems. Zbl 0801.90108
Kojima, Masakazu; Megiddo, Nimrod; Mizuno, Shinji
1993
Large-step interior point algorithms for linear complementarity problems. Zbl 0781.90085
Kojima, Masakazu; Kurita, Yoshifumi; Mizuno, Shinji
1993
A little theorem of the big $${\mathcal M}$$ in interior point algorithms. Zbl 0793.90083
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1993
On the big $${\mathcal M}$$ in the affine scaling algorithm. Zbl 0804.90088
Ishihara, Tohru; Kojima, Masakazu
1993
An interior point potential reduction algorithm for the linear complementarity problem. Zbl 0764.90083
Kojima, Masakazu; Megiddo, Nimrod; Ye, Yinyu
1992
A unified approach to interior point algorithms for linear complementarity problems: A summary. Zbl 0745.90069
Kojima, Masakazu; Megiddo, Nimrod; Noma, Toshihito; Yoshise, Akiko
1991
An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems. Zbl 0738.90077
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1991
A unified approach to interior point algorithms for linear complementary problems. Zbl 0766.90077
Kojima, Masakazu (ed.); Megiddo, Nimrod (ed.); Noma, Toshihito (ed.); Yoshise, Akiko (ed.)
1991
Homotopy continuation methods for nonlinear complementarity problems. Zbl 0744.90087
Kojima, Masakazu; Megiddo, Nimrod; Noma, Toshihito
1991
The relation between the path of centers and Smale’s regularization of the linear programming problem. Zbl 0727.65053
Kojima, Masakazu; Megiddo, Nimrod
1991
Limiting behavior of trajectories generated by a continuation method for monotone complementarity problems. Zbl 0719.90085
Kojima, Masakazu; Mizuno, Shinji; Noma, Toshihito
1990
Ellipsoids that contain all the solutions of a positive semi-definite linear complementarity problem. Zbl 0723.90079
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1990
A polynomial-time algorithm for a class of linear complementarity problems. Zbl 0676.90087
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1989
A primal-dual interior point algorithm for linear programming. Zbl 0708.90049
Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
1989
A new continuation method for complementarity problems with uniform P- functions. Zbl 0673.90084
Kojima, Masakazu; Mizuno, Shinji; Noma, Toshihito
1989
A dual interior primal simplex method for linear programming. Zbl 0658.90062
Tamura, Akihisa; Takehara, Hitoshi; Fukuda, Komei; Fujishige, Satoru; Kojima, Masakazu
1988
Recovering optimal dual solutions in Karmarkar’s polynomial algorithm for linear programming. Zbl 0639.90062
Ye, Yinyu; Kojima, Masakazu
1987
Extension of Newton and quasi-Newton methods to systems of $$PC^ 1$$ equations. Zbl 0611.65032
Kojima, Masakazu; Shindo, Susumu
1986
Determining basic variables of optimal solutions in Karmarkar’s new LP algorithm. Zbl 0661.90057
Kojima, Masakazu
1986
Strongly stable equilibrium points of n-person noncooperative games. Zbl 0581.90098
Kojima, M.; Okada, A.; Shindoh, S.
1985
A PL homotopy continuation method with the use of an odd map for the artificial level. Zbl 0593.65038
Kojima, M.; Oishi, S.; Sumi, Y.; Horiuchi, K.
1985
Continuous deformation of nonlinear programs. Zbl 0569.90074
Kojima, Masakazu; Hirabayashi, Ryuichi
1984
A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. Zbl 0539.65036
Kojima, Masakazu; Yamamoto, Yoshitsugu
1984
Computation of all solutions to a system of polynomial equations. Zbl 0517.90062
Kojima, Masakazu; Mizuno, Shinji
1983
Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods. Zbl 0509.90070
Kojima, Masakazu; Yamamoto, Yoshitsugu
1982
On the calculation of Stokes’ flow past porous particles. Zbl 0484.76049
Higdon, J. J. L.; Kojima, M.
1981
An introduction to variable dimension algorithms for solving systems of equations. Zbl 0471.65030
Kojima, Masakazu
1981
On the number of solutions to a class of complementarity problems. Zbl 0461.90066
Kojima, M.; Saigal, Romesh
1981
...and 14 more Documents
all top 5

#### Cited by 1,599 Authors

 50 Kojima, Masakazu 37 Ye, Yinyu 35 Kheirfam, Behrouz 23 Lasserre, Jean-Bernard 21 Kim, Sunyoung 19 Mizuno, Shinji 19 Roos, Cornelis 18 Potra, Florian-Alexandru 18 Terlaky, Tamás 18 Todd, Michael J. 18 Zangiabadi, Maryam 15 Mansouri, Hossein 15 Wang, Guoqiang 14 Pang, Jong-Shi 13 Bai, Yanqin 13 Darvay, Zsolt 13 Qi, Liqun 13 Tunçel, Levent 12 Huang, Zheng-Hai 12 Liu, Hongwei 12 Monteiro, Renato D. C. 12 Yamashita, Makoto 11 Anstreicher, Kurt M. 11 Muramatsu, Masakazu 11 Zhang, Yin 10 Megiddo, Nimrod 10 Pirhaji, Mohammad 10 Zangiabadi, Mostafa 9 Gowda, Muddappa Seetharama 9 Júdice, Joaquim João 9 Liu, Changhe 9 Mansouri, Hosseino 9 Mitchell, John E. 9 Sturm, Jos F. 9 Toh, Kim-Chuan 9 Tsuchiya, Takashi 9 Yamamoto, Yoshitsugu 8 Asadi, Soodabeh 8 Burer, Samuel 8 Cho, Gyeong-Mi 8 Fang, Shu-Cherng 8 Kanno, Yoshihiro 8 Sun, Jie 8 Yoshise, Akiko 8 Zhang, Mingwang 8 Zhang, Shuzhong 7 Anjos, Miguel F. 7 Gondzio, Jacek 7 Han, Jiye 7 Henrion, Didier 7 Illés, Tibor 7 Jongen, Hubertus Th. 7 Li, Duan 7 Tapia, Richard A. 7 Tseng, Paul 7 Waki, Hayato 7 Wolkowicz, Henry 7 Xu, Chengxian 7 Yu, Bo 7 Zhao, Yunbin 6 Cerone, Vito 6 Cottle, Richard W. 6 Dang, Chuangyin 6 D’Apuzzo, Marco 6 Harker, Patrick T. 6 Jarre, Florian 6 Kanzow, Christian 6 Lesaja, Goran 6 Letchford, Adam N. 6 Magron, Victor 6 Mansouri, Hossien 6 Nakata, Kazuhide 6 Nie, Jiawang 6 Peyghami, Mohammad Reza 6 Povh, Janez 6 Regruto, Diego 6 Van der Laan, Gerard 5 Alzalg, Baha M. 5 de Klerk, Etienne 5 De Simone, Valentina 5 den Hertog, Dick 5 Deng, Zhibin 5 Dey, Santanu S. 5 di Serafino, Daniela 5 Gonzaga, Clovis C. 5 Guddat, Jürgen 5 Jeyakumar, Vaithilingam 5 Klep, Igor 5 Kohr, Mirela 5 Kortanek, Kenneth O. 5 Li, Guoyin 5 Luo, ZiYan 5 Mahdavi-Amiri, Nezam 5 Martínez, José Mario 5 Mehta, Dhagash 5 Pang, Liping 5 Qi, Houduo 5 Rigó, Petra Renáta 5 Rustem, Berc 5 Saigal, Romesh ...and 1,499 more Authors
all top 5

#### Cited in 202 Serials

 207 Mathematical Programming. Series A. Series B 112 Journal of Optimization Theory and Applications 56 Computational Optimization and Applications 54 Journal of Global Optimization 52 Optimization Methods & Software 49 Linear Algebra and its Applications 42 Optimization 35 European Journal of Operational Research 33 Mathematical Programming 32 SIAM Journal on Optimization 31 Journal of Computational and Applied Mathematics 31 Annals of Operations Research 29 Operations Research Letters 25 Applied Mathematics and Computation 24 Optimization Letters 19 Numerical Algorithms 16 Mathematical Programming Computation 13 Automatica 12 Computers & Mathematics with Applications 12 Discrete Applied Mathematics 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Journal of the Operations Research Society of China 10 Theoretical Computer Science 10 Computers & Operations Research 9 RAIRO. Operations Research 8 Applied Numerical Mathematics 8 Acta Mathematicae Applicatae Sinica. English Series 8 Mathematical Problems in Engineering 8 Journal of Industrial and Management Optimization 7 Computer Methods in Applied Mechanics and Engineering 7 Journal of Mathematical Analysis and Applications 7 Journal of Symbolic Computation 7 Journal of Applied Mathematics and Computing 7 Asian-European Journal of Mathematics 6 Journal of Fluid Mechanics 6 Asia-Pacific Journal of Operational Research 6 SIAM Journal on Matrix Analysis and Applications 6 Science in China. Series A 6 Japan Journal of Industrial and Applied Mathematics 6 Numerical Algebra, Control and Optimization 5 International Journal of Control 5 International Journal of Game Theory 5 Kybernetika 5 Numerical Functional Analysis and Optimization 5 Algorithmica 5 International Journal of Robust and Nonlinear Control 5 Mathematical Methods of Operations Research 5 Wuhan University Journal of Natural Sciences (WUJNS) 5 Discrete Optimization 4 Mathematics of Computation 4 Mathematics of Operations Research 4 ZOR. Zeitschrift für Operations Research 4 Top 4 Acta Mathematica Sinica. English Series 4 CEJOR. Central European Journal of Operations Research 4 Optimization and Engineering 4 Journal of Applied Mathematics 4 Journal of Mathematical Modelling and Algorithms in Operations Research 3 Applied Mathematics and Optimization 3 Computing 3 Journal of Information & Optimization Sciences 3 Discrete & Computational Geometry 3 Applied Mathematics Letters 3 International Journal of Computer Mathematics 3 Computational and Applied Mathematics 3 European Journal of Control 3 Journal of High Energy Physics 3 Journal of Systems Science and Complexity 3 Afrika Matematika 3 EURO Journal on Computational Optimization 2 Bulletin of the Australian Mathematical Society 2 Linear and Multilinear Algebra 2 Mathematical Biosciences 2 Periodica Mathematica Hungarica 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Journal of Computer and System Sciences 2 Meccanica 2 Operations Research 2 Transactions of the American Mathematical Society 2 Applied Mathematics and Mechanics. (English Edition) 2 Journal of Scientific Computing 2 Neural Computation 2 Applied Mathematical Modelling 2 SIAM Review 2 SIAM Journal on Scientific Computing 2 Applied Mathematics. Series B (English Edition) 2 Physics of Fluids 2 Numerical Linear Algebra with Applications 2 International Transactions in Operational Research 2 Journal of Inequalities and Applications 2 International Game Theory Review 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Computational Management Science 2 Frontiers of Mathematics in China 2 Set-Valued and Variational Analysis 2 Croatian Operational Research Review (CRORR) 2 Computer Science Review 2 Nonlinear Analysis. Theory, Methods & Applications 2 International Journal of Systems Science. Principles and Applications of Systems and Integration 1 Acta Mechanica ...and 102 more Serials
all top 5

#### Cited in 53 Fields

 1,139 Operations research, mathematical programming (90-XX) 306 Numerical analysis (65-XX) 114 Calculus of variations and optimal control; optimization (49-XX) 60 Linear and multilinear algebra; matrix theory (15-XX) 47 Computer science (68-XX) 45 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 38 Systems theory; control (93-XX) 33 Algebraic geometry (14-XX) 27 Fluid mechanics (76-XX) 21 Convex and discrete geometry (52-XX) 19 Operator theory (47-XX) 19 Mechanics of deformable solids (74-XX) 18 Commutative algebra (13-XX) 15 Combinatorics (05-XX) 15 Field theory and polynomials (12-XX) 11 Number theory (11-XX) 11 Real functions (26-XX) 10 General topology (54-XX) 9 Nonassociative rings and algebras (17-XX) 9 Partial differential equations (35-XX) 9 Statistics (62-XX) 9 Quantum theory (81-XX) 8 Ordinary differential equations (34-XX) 7 Mechanics of particles and systems (70-XX) 7 Information and communication theory, circuits (94-XX) 6 Algebraic topology (55-XX) 6 Probability theory and stochastic processes (60-XX) 5 Mathematical logic and foundations (03-XX) 5 Functions of a complex variable (30-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Functional analysis (46-XX) 5 Manifolds and cell complexes (57-XX) 5 Biology and other natural sciences (92-XX) 4 General algebraic systems (08-XX) 4 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 3 Differential geometry (53-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)