A unification of the existence theorems of the nonlinear complementarity problem. - Masakazu Kojima (Math. Program., 1975)

On the existence and uniqueness of solutions in nonlinear complementarity theory. - Nimrod Megiddo; Masakazu Kojima (Math. Program., 1977)

Studies on Piecewise-Linear Approximations of Piecewise-C1 Mappings in Fixed Points and Complementarity Theory. - Masakazu Kojima (Math. Oper. Res., 1978)

A modification of todd's triangulation J3. - Masakazu Kojima (Math. Program., 1978)

A Complementary Pivoting Approach to Parametric Nonlinear Programming. - Masakazu Kojima (Math. Oper. Res., 1979)

A PL homotopy for finding all the roots of a polynomial. - Masakazu Kojima; Hisakazu Nishino; Naohiko Arima (Math. Program., 1979)

On the number of solutions to a class of linear complementarity problems. - Masakazu Kojima; Romesh Saigal (Math. Program., 1979)

On the number of solutions to a class of complementarity problems. - Masakazu Kojima; Romesh Saigal (Math. Program., 1981)

Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods. - Masakazu Kojima; Yoshitsugu Yamamoto (Math. Program., 1982)

Computation of all solutions to a system of polynomial equations. - Masakazu Kojima; Shinji Mizuno (Math. Program., 1983)

A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm. - Masakazu Kojima; Yoshitsugu Yamamoto (Math. Program., 1984)

Strongly Stable Equilibrium Points of N-Person Noncooperative Games. - Masakazu Kojima; Akira Okada; Susumu Shindoh (Math. Oper. Res., 1985)

A PL homotopy continuation method with the use of an odd map for the artificial level. - Masakazu Kojima; Shin'ichi Oishi; Yuzo Sumi; Kazuo Horiuchi (Math. Program., 1985)

Determining Basic Variables of Optimal Solutions in Karmarkar's New LP Algorithm. - Masakazu Kojima (Algorithmica, 1986)

Recovering optimal dual solutions in Karmarkar's polynomial algorithm for linear programming. - Yinyu Ye 001; Masakazu Kojima (Math. Program., 1987)

A new continuation method for complementarity problems with uniformP-functions. - Masakazu Kojima; Shinji Mizuno; Toshihito Noma (Math. Program., 1989)

A polynomial-time algorithm for a class of linear complementarity problems. - Masakazu Kojima; Shinji Mizuno; Akiko Yoshise (Math. Program., 1989)

Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems. - Masakazu Kojima; Shinji Mizuno; Toshihito Noma (Math. Oper. Res., 1990)

Ellipsoids that Contain All the Solutions of a Positive Semi-Definite Linear Complementarity Problem. - Masakazu Kojima; Shinji Mizuno; Akiko Yoshise (Math. Program., 1990)

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems - Masakazu Kojima; Nimrod Megiddo; Toshihito Noma; Akiko Yoshise (Springer, 1991)

Homotopy Continuation Methods for Nonlinear Complementarity Problems. - Masakazu Kojima; Nimrod Megiddo; Toshihito Noma (Math. Oper. Res., 1991)

An O(square root(n) * L) iteration potential reduction algorithm for linear complementarity problems. - Masakazu Kojima; Shinji Mizuno; Akiko Yoshise (Math. Program., 1991)

A unified approach to interior point algorithms for linear complementarity problems: A summary. - Masakazu Kojima; Nimrod Megiddo; Toshihito Noma; Akiko Yoshise (Oper. Res. Lett., 1991)

An interior point potential reduction algorithm for the linear complementarity problem. - Masakazu Kojima; Nimrod Megiddo; Yinyu Ye 001 (Math. Program., 1992)

A General Framework of Continuation Methods for Complementarity Problems. - Masakazu Kojima; Nimrod Megiddo; Shinji Mizuno (Math. Oper. Res., 1993)

On the big Mu in the affine scaling algorithm. - Tohru Ishihara; Masakazu Kojima (Math. Program., 1993)

Theoretical convergence of large-step primal-dual interior point algorithms for linear programming. - Masakazu Kojima; Nimrod Megiddo; Shinji Mizuno (Math. Program., 1993)

A primal-dual infeasible-interior-point algorithm for linear programming. - Masakazu Kojima; Nimrod Megiddo; Shinji Mizuno (Math. Program., 1993)

A little theorem of the big Mu in interior point algorithms. - Masakazu Kojima; Shinji Mizuno; Akiko Yoshise (Math. Program., 1993)

Large-Step Interior Point Algorithms for Linear Complementarity Problems. - Masakazu Kojima; Yoshifumi Kurita; Shinji Mizuno (SIAM J. Optim., 1993)

Global convergence in infeasible-interior-point algorithms. - Masakazu Kojima; Toshihito Noma; Akiko Yoshise (Math. Program., 1994)

Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming. - Shinji Mizuno; Masakazu Kojima; Michael J. Todd (SIAM J. Optim., 1995)

Basic lemmas in polynomial-time infeasible-interiorpoint methods for linear programs. - Masakazu Kojima (Ann. Oper. Res., 1996)

A Generalized Convexity and Variational Inequality for Quasi-Convex Minimization. - Phan Thien Thach; Masakazu Kojima (SIAM J. Optim., 1996)

Semidefinite Programming Relaxation for Nonconvex Quadratic Programs. - Tetsuya Fujie; Masakazu Kojima (J. Glob. Optim., 1997)

Centers of Monotone Generalized Complementarity Problems. - Masayuki Shida; Susumu Shindoh; Masakazu Kojima (Math. Oper. Res., 1997)

Exploiting sparsity in primal-dual interior-point methods for semidefinite programming. - Katsuki Fujisawa; Masakazu Kojima; Kazuhide Nakata (Math. Program., 1997)

Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices. - Masakazu Kojima; Susumu Shindoh; Shinji Hara (SIAM J. Optim., 1997)

Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs. - Masakazu Kojima; Masayuki Shida; Susumu Shindoh (Math. Program., 1998)

Existence and Uniqueness of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP. - Masayuki Shida; Susumu Shindoh; Masakazu Kojima (SIAM J. Optim., 1998)

Search directions in the SDP and the monotone SDLCP: generalization and inexact computation. - Masakazu Kojima; Masayuki Shida; Susumu Shindoh (Math. Program., 1999)

A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton Search Direction. - Masakazu Kojima; Masayuki Shida; Susumu Shindoh (SIAM J. Optim., 1999)

Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization. - Masakazu Kojima; Levent Tunçel (Math. Program., 2000)

Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets. - Masakazu Kojima; Levent Tunçel (SIAM J. Optim., 2000)

Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem. - Mituhiro Fukuda; Masakazu Kojima (Comput. Optim. Appl., 2001)

Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets. - Masakazu Kojima; Akiko Takeda (Math. Oper. Res., 2001)

Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework. - Mituhiro Fukuda; Masakazu Kojima; Kazuo Murota; Kazuhide Nakata (SIAM J. Optim., 2001)

On the finite convergence of successive SDP relaxation methods. - Masakazu Kojima; Levent Tunçel (Eur. J. Oper. Res., 2002)

Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems. - Masakazu Kojima; Levent Tunçel (J. Glob. Optim., 2002)

Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems. - Akiko Takeda; Katsuki Fujisawa; Yusuke Fukaya; Masakazu Kojima (J. Glob. Optim., 2002)

Lagrangian Dual Interior-Point Methods for Semidefinite Programs. - Mituhiro Fukuda; Masakazu Kojima; Masayuki Shida (SIAM J. Optim., 2002)

Solving Some Large Scale Semidefinite Programs via the Conjugate Residual Method. - Kim-Chuan Toh; Masakazu Kojima (SIAM J. Optim., 2002)

Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations. - Sunyoung Kim; Masakazu Kojima (Comput. Optim. Appl., 2003)

Second order cone programming relaxation of a positive semidefinite constraint. - Sunyoung Kim; Masakazu Kojima; Makoto Yamashita (Optim. Methods Softw., 2003)

Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0). - Makoto Yamashita; Katsuki Fujisawa; Masakazu Kojima (Optim. Methods Softw., 2003)

SDPARA: SemiDefinite Programming Algorithm paRAllel version. - Makoto Yamashita; Katsuki Fujisawa; Masakazu Kojima (Parallel Comput., 2003)

High Performance Grid and Cluster Computing for Some Optimization Problems. - Katsuki Fujisawa; Masakazu Kojima; Akiko Takeda; Makoto Yamashita (SAINT Workshops, 2004)

PHoM - a Polyhedral Homotopy Continuation Method for Polynomial Systems. - Takayuki Gunji; Sunyoung Kim; Masakazu Kojima; Akiko Takeda; Katsuki Fujisawa; Tomohiko Mizutani (Computing, 2004)

Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods. - Sunyoung Kim; Masakazu Kojima (Computing, 2004)

Sparsity in sums of squares of polynomials. - Masakazu Kojima; Sunyoung Kim; Hayato Waki (Math. Program., 2005)

Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems. - Sunyoung Kim; Masakazu Kojima; Hayato Waki (SIAM J. Optim., 2005)

PHoMpara - Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems. - Takayuki Gunji; Sunyoung Kim; Katsuki Fujisawa; Masakazu Kojima (Computing, 2006)

A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion. - Kazuhide Nakata; Makoto Yamashita; Katsuki Fujisawa; Masakazu Kojima (Parallel Comput., 2006)

Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity. - Hayato Waki; Sunyoung Kim; Masakazu Kojima; Masakazu Muramatsu (SIAM J. Optim., 2006)

A conversion of an SDP having free variables into the standard form SDP. - Kazuhiro Kobayashi; Kazuhide Nakata; Masakazu Kojima (Comput. Optim. Appl., 2007)

Dynamic Enumeration of All Mixed Cells. - Tomohiko Mizutani; Akiko Takeda; Masakazu Kojima (Discret. Comput. Geom., 2007)

An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones. - Masakazu Kojima; Masakazu Muramatsu (Math. Program., 2007)

Algorithm 883: SparsePOP - A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems. - Hayato Waki; Sunyoung Kim; Masakazu Kojima; Masakazu Muramatsu; Hiroshi Sugimoto (ACM Trans. Math. Softw., 2008)

A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones. - Masakazu Kojima; Masakazu Muramatsu (Comput. Optim. Appl., 2009)

Recognizing underlying sparsity in optimization. - Sunyoung Kim; Masakazu Kojima; Philippe L. Toint (Math. Program., 2009)

Exploiting Sparsity in SDP Relaxation for Sensor Network Localization. - Sunyoung Kim; Masakazu Kojima; Hayato Waki (SIAM J. Optim., 2009)

Semidefinite programming relaxations for sensor network localization. - Sunyoung Kim; Masakazu Kojima (CACSD, 2010)

Exploiting Structured Sparsity in Large Scale Semidefinite Programming Problems. - Masakazu Kojima (ICMS, 2010)

Sdp Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems. - Martin Mevissen; Masakazu Kojima (Asia Pac. J. Oper. Res., 2010)

Solving polynomial least squares problems via semidefinite programming relaxations. - Sunyoung Kim; Masakazu Kojima (J. Glob. Optim., 2010)

Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion. - Sunyoung Kim; Masakazu Kojima; Martin Mevissen; Makoto Yamashita (Math. Program., 2011)

Algorithm 920: SFSDP: A Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems. - Sunyoung Kim; Masakazu Kojima; Hayato Waki; Makoto Yamashita (ACM Trans. Math. Softw., 2012)

Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization. - Masakazu Kojima; Makoto Yamashita (Math. Program., 2013)

A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming. - Naohiko Arima; Sunyoung Kim; Masakazu Kojima (SIAM J. Optim., 2013)

Faster, but weaker, relaxations for quadratically constrained quadratic programs. - Samuel Burer; Sunyoung Kim; Masakazu Kojima (Comput. Optim. Appl., 2014)

Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization. - Naohiko Arima; Sunyoung Kim; Masakazu Kojima (J. Optim. Theory Appl., 2016)

A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. - Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (Math. Program., 2016)

A robust Lagrangian-DNN method for a class of quadratic optimization problems. - Naohiko Arima; Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (Comput. Optim. Appl., 2017)

Binary quadratic optimization problems that are difficult to solve by conic relaxations. - Sunyoung Kim; Masakazu Kojima (Discret. Optim., 2017)

Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems. - Naoki Ito; Sunyoung Kim; Masakazu Kojima; Akiko Takeda; Kim-Chuan Toh (J. Glob. Optim., 2018)

Algorithm 996: BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems With Binary, Box, and Complementarity Constraints. - Naoki Ito; Sunyoung Kim; Masakazu Kojima; Akiko Takeda; Kim-Chuan Toh (ACM Trans. Math. Softw., 2019)

Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures. - Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (J. Glob. Optim., 2020)

A Geometrical Analysis on Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems. - Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (SIAM J. Optim., 2020)

A Newton-bracketing method for a simple conic optimization problem. - Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (Optim. Methods Softw., 2021)

Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints. - Sunyoung Kim; Masakazu Kojima; Kim-Chuan Toh (Math. Program., 2022)

Further Development in Convex Conic Reformulation of Geometric Nonconvex Conic Optimization Problems. - Naohiko Arima; Sunyoung Kim; Masakazu Kojima (SIAM J. Optim., 2024)

Equivalent sufficient conditions for global optimality of quadratically constrained quadratic programs. - Sunyoung Kim; Masakazu Kojima (Math. Methods Oper. Res., 2025)

An exceptionally difficult binary quadratic optimization problem with symmetry: a challenge for the largest unsolved QAP instance Tai256c. - Koichi Fujii; Sunyoung Kim; Masakazu Kojima; Hans D. Mittelmann; Yuji Shinano (Optim. Lett., 2025)