Masakazu Kojima

Masakazu Kojima's AcademicInfluence.com Rankings

Masakazu Kojima

Mathematics

#7479

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#10165

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Measure Theory

#2212

World Rank

#2659

Historical Rank

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Mathematics

Masakazu Kojima's Degrees

PhD Mathematics Kyoto University

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Masakazu Kojima's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems (1991) (592)
A primal-dual interior point algorithm for linear programming (1988) (529)
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity (2006) (448)
Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices (1997) (445)
A polynomial-time algorithm for a class of linear complementarity problems (1989) (359)
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework (2000) (324)
Strongly Stable Stationary Solutions in Nonlinear Programs. (1980) (320)
A primal—dual infeasible-interior-point algorithm for linear programming (1993) (291)
Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0) (2003) (202)
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming (1997) (191)
Algorithm 883: SparsePOP---A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems (2008) (185)
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations (2003) (174)
Semidefinite Programming Relaxation for Nonconvex Quadratic Programs (1997) (170)
EXTENSION OF NEWTON AND QUASI-NEWTON METHODS TO SYSTEMS OF PC^1 EQUATIONS (1986) (148)
An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems (1991) (148)
Second order cone programming relaxation of nonconvex quadratic optimization problems (2001) (140)
Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs (1998) (135)
SDPA (SemiDefinite Programming Algorithm) User's Manual Version 6.2.0 (1995) (133)
Interior Point Methods for the Monotone Linear Complementarity Problem in Symmetric Matrices (1995) (127)
Homotopy Continuation Methods for Nonlinear Complementarity Problems (1991) (124)
Branch-and-Cut Algorithms for the Bilinear Matrix Inequality Eigenvalue Problem (2001) (121)
Sums of Squares Relaxations of Polynomial Semidefinite Programs (2003) (120)
Sparsity in sums of squares of polynomials (2005) (118)
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion (2011) (114)
PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems (2004) (113)
Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets (1999) (96)
Exploiting Sparsity in SDP Relaxation for Sensor Network Localization (2009) (92)
A numerical algorithm for block-diagonal decomposition of matrix $${*}$$-algebras with application to semidefinite programming (2010) (85)
A new continuation method for complementarity problems with uniformP-functions (1989) (82)
Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems (1990) (77)
SDPARA: SemiDefinite Programming Algorithm paRAllel version (2003) (76)
Recovering optimal dual solutions in Karmarkar's polynomial algorithm for linear programming (1987) (76)
An interior point potential reduction algorithm for the linear complementarity problem (1992) (74)
Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems (2005) (72)
Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming (1995) (71)
Continuous deformation of nonlinear programs (1984) (70)
A Lagrangian–DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems (2016) (67)
A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton Search Direction (1999) (62)
Solving Some Large Scale Semidefinite Programs via the Conjugate Residual Method (2002) (62)
Numerical Evaluation of SDPA (Semidefinite Programming Algorithm) (2000) (61)
On the existence and uniqueness of solutions in nonlinear complementarity theory (1977) (56)
Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods (1982) (54)
A General Framework of Continuation Methods for Complementarity Problems (1993) (53)
A unification of the existence theorems of the nonlinear complementarity problem (1975) (51)
Theoretical convergence of large-step primal—dual interior point algorithms for linear programming (1993) (51)
Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization (2000) (49)
A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones (2003) (49)
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones (2009) (46)
An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones (2007) (44)
Global convergence in infeasible-interior-point algorithms (1994) (43)
Search directions in the SDP and the monotone SDLCP: generalization and inexact computation (1999) (43)
Existence and Uniqueness of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP (1998) (41)
A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm (1984) (41)
SDPA-M (SemiDefinite Programming Algorithm in MATLAB) User's Manual — Version 6.2.0 (2003) (40)
Computing all nonsingular solutions of cyclic- n polynomial using polyhedral homotopy continuation methods (2003) (40)
A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming (2013) (39)
Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP (2008) (36)
B-453 User's Manual for SparseCoLO: Conversion Methods for SPARSE COnic-form Linear Optimization Problems (2009) (36)
SDPA (SemiDefinite Programming Algorithm) (1999) (35)
Dynamic Enumeration of All Mixed Cells (2007) (35)
Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint (2003) (34)
B-411 Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity (2004) (31)
ENUMERATION OF ALL SOLUTIONS OF A COMBINATORIAL LINEAR INEQUALITY SYSTEM ARISING FROM THE POLYHEDRAL HOMOTOPY CONTINUATION METHOD (2002) (31)
Strongly Stable Equilibrium Points of N-Person Noncooperative Games (1985) (30)
On the homotopic approach to systems of equations with separable mappings (1978) (30)
A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion (2006) (29)
On the number of solutions to a class of linear complementarity problems (1978) (27)
B-475 Lagrangian-Conic Relaxations, Part I: A Unified Framework and Its Applications to Quadratic Optimization Problems (2014) (24)
Algorithm 920: SFSDP: A Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems (2012) (24)
A unified approach to interior point algorithms for linear complementarity problems: A summary (1991) (23)
Linear Algebra for Semidefinite Programming (1997) (22)
Studies on Piecewise-Linear Approximations of Piecewise-C1 Mappings in Fixed Points and Complementarity Theory (1978) (22)
Lagrangian Dual Interior-Point Methods for Semidefinite Programs (2002) (22)
SIMPLIFIED COPOSITIVE AND LAGRANGIAN RELAXATIONS FOR LINEARLY CONSTRAINED QUADRATIC OPTIMIZATION PROBLEMS IN CONTINUOUS AND BINARY VARIABLES (2017) (22)
Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods (2004) (21)
A little theorem of the bigℳ in interior point algorithms (1993) (21)
Large-Step Interior Point Algorithms for Linear Complementarity Problems (1993) (20)
A Complementary Pivoting Approach to Parametric Nonlinear Programming (1979) (19)
SDPA-C (SemiDefinite Programming Algorithm - Completion method) User's Manual — Version 6.2.0 (2004) (19)
On the Relationship Between Conditions that Insure a PL Mapping is a Homeomorphism (1980) (19)
Faster, but weaker, relaxations for quadratically constrained quadratic programs (2014) (19)
Solving partial differential equations via sparse SDP relaxations (2007) (18)
A Study of ${\text{PC}}^1 $ Homeomorphisms on Subdivided Polyhedrons (1979) (18)
REDUCTION OF MONOTONE LINEAR COMPLEMENTARITY PROBLEMS OVER CONES TO LINEAR PROGRAMS OVER CONES (1997) (18)
A PL homotopy for finding all the roots of a polynomial (1979) (18)
User Manual for SFSDP: a Sparse Version of Full SemiDefinite Programming Relaxation for Sensor Network Localization Problems (2009) (17)
PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems (2006) (17)
On the finite convergence of successive SDP relaxation methods (2002) (16)
A note on the Nesterov-Todd and the Kojima-Shindoh-hara search directions in semidefinite programming (1999) (16)
An introduction to variable dimension algorithms for solving systems of equations (1981) (16)
On the number of solutions to a class of complementarity problems (1981) (16)
Computation of all solutions to a system of polynomial equations (1983) (15)
Horizontal and vertical decomposition in interior point methods for linear programs (1994) (15)
Recognizing underlying sparsity in optimization (2009) (14)
A robust Lagrangian-DNN method for a class of quadratic optimization problems (2017) (14)
An Extension of Lemke’s Method to the Piecewise Linear Complementarity Problem (1976) (13)
Parallel Implementation of Successive Convex Relaxation Methods for Quadratic Optimization Problems (2002) (12)
Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems (2012) (12)
High performance grid and cluster computing for some optimization problems (2004) (12)
Sdp Relaxations for Quadratic Optimization Problems Derived from Polynomial Optimization Problems (2010) (12)
A conversion of an SDP having free variables into the standard form SDP (2007) (11)
Basic lemmas in polynomial-time infeasible-interiorpoint methods for linear programs (1996) (10)
Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets (2001) (10)
EFFICIENT EVALUATION OF POLYNOMIALS AND THEIR PARTIAL DERIVATIVES IN HOMOTOPY CONTINUATION METHODS (2008) (10)
Centers of Monotone Generalized Complementarity Problems (1997) (10)
B-471 Extension of Completely Positive Cone Relaxation to Polynomial Optimization (2013) (10)
Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization (2016) (10)
A modification of todd's triangulationJ3 (1978) (9)
A Newton-bracketing method for a simple conic optimization problem (2019) (9)
Solving polynomial least squares problems via semidefinite programming relaxations (2010) (8)
Interior-Point Methods for Lagrangian Duals of Semidefinite Programs (2000) (8)
A DUAL INTERIOR PRIMAL SIMPLEX METHOD FOR LINEAR PROGRAMMING (1988) (8)
CMPSm : A Continuation Method for Polynomial Systems (MATLAB version) — User's Manual (2002) (8)
SOLVING LARGE SCALE OPTIMIZATION PROBLEMS VIA GRID AND CLUSTER COMPUTING( Network Design, Control and Optimization) (2004) (8)
Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems (1999) (7)
SPARSE SECOND ORDER CONE PROGRAMMING FORMULATIONS FOR CONVEX OPTIMIZATION PROBLEMS (2008) (7)
Binary quadratic optimization problems that are difficult to solve by conic relaxations (2017) (6)
A Generalized Convexity and Variational Inequality for Quasi-Convex Minimization (1996) (6)
Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems (2017) (6)
A Study of PCl Homeomorphisms on Subdivided Polyhedrons (1978) (6)
The Relation Between the Path of Centers and Smale's Regularization of the Linear Programming Problem (1991) (6)
Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures (2019) (6)
SOLVING LARGE SCALE OPTIMIZA . TION PROBLEMS VIA GRID AND CLUSTER COMPUTING (2003) (5)
Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems (2001) (5)
Algorithm 996 (2018) (5)
A Geometrical Analysis on Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems (2020) (5)
Monotonicity of primal–dual interior-point algorithms for semidefinite programming problems (1998) (5)
Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming (2002) (5)
LAGRANGIAN-CONIC RELAXATIONS, PART II: APPLICATIONS TO POLYNOMIAL OPTIMIZATION PROBLEMS (2020) (4)
A property of matrices with positive determinants (1980) (4)
Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints (2020) (4)
Semidefinite programming relaxations for sensor network localization (2010) (4)
A NUMERICAL METHOD FOR SURVIVAL PROBABILITY OF DIFFUSION PROCESSES USING SEMIDEFINITE PROGRAMMING (2008) (4)
EQUALITY BASED CONTRACTION OF SEMIDEFINITE PROGRAMMING RELAXATIONS IN POLYNOMIAL OPTIMIZATION (2008) (4)
CMPSc : A Continuation Method for Polynomial Systems (C++ version) (2002) (3)
B-414 User Manual for SparsePOP: a Sparse Semidefinite Programming Relax- ation of Polynomial Optimization Problems (2009) (3)
A Lagrangian–DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems (2015) (3)
Solving Challenging Large Scale QAPs (2021) (3)
On the bigℳ in the affine scaling algorithm (1993) (3)
A Geometrical Analysis of a Class of Nonconvex Conic Programs for Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems (2019) (3)
Determining basic variables of optimal solutions in Karmarkar's new LP algorithm (1986) (3)
A Lagrangian Relaxation Method for Approximating the Analytic Center of a Polytope (1992) (2)
Parallel Primal‐Dual Interior‐Point Methods for SemiDefinite Programs (2006) (2)
A generalized convexity and a homotopy approach to a quasiconvex minimization(Nonlinear Analysis and Mathematical Economics) (1994) (2)
Ellipsoids that contain all the solutions of a positive semi-definite linear complementarity problem (1990) (2)
Invariance under affine transformation in semidefinite programming relaxation for polynomial optimization problems (2009) (2)
User Manual for SparsePOP : a Sparse Semidefinite Programming Relaxation of P polynomial O ptimization P roblems (2005) (2)
Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization (2013) (2)
A Continuation Method for Large-sized Sensor Network Localization Problems (2011) (2)
Computational Prospects on Copositive Programming(Theory of Modeling and Optimization) (2006) (2)
Sparsity in a Sum of Squares of Polynomials (2003) (2)
User manual of NewtBracket: “A Newton-Bracketing method for a simple conic optimization problem” [10] with applications to QOPs in binary variables (2020) (2)
Relaxations of Sparse Polynomial Optimization Problems (2003) (2)
Solving some large s ale semide niteprograms via the onjugate residual (2000) (2)
A PL homotopy continuation method with the use of an odd map for the artificial level (1985) (2)
IMPROVING THE COMPUTATIONAL EFFICIENCY OF FIXED POINT ALGORITHMS (1984) (1)
Parallel Implementation of Successive Sparse SDP Relaxations for Large-Scale Euclidean Distance Geometry Problems (2012) (1)
Research Reports on Mathematical and Computing Sciences Series B : Operations Research (2003) (1)
A Primitive Interior Point Algorithm for Semidefinite Programs in (1994) (1)
Exploiting Structured Sparsity in Large Scale Semidefinite Programming Problems (2010) (1)
Strong duality of a conic optimization problem with a single hyperplane and two cone constraints (2021) (1)
An Algorithm for Decomposition of Matrix *-Algebras Generated by Symmetric Matrices (Mathematical Programming in the 21st Century : Optimization Modeling and Algorithms) (2009) (1)
Strong duality of a conic optimization problem with two cones and a single equality constraint (2021) (1)
A Unified Parametric Quadratic Programming Solution to some Stochastic Linear Programming Models. (1978) (1)
Semidefinite Programming Relaxation and Lagrangian Relaxation for Polynomial Optimization Problems (2003) (0)
Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization (2015) (0)
A Combinatorial Problem Arising from Polyhedral Homotopies for Solving Polynomial Systems (Mathematical Science of Optimization) (2000) (0)
SDPA Project and New Features of SDPA 7.1.0 (High Performance Algorithms for Computational Science and Their Applications) (2008) (0)
A MODIFICATION O F T ODD'S T RIANGULATION J3 (1978) (0)
Faster, but weaker, relaxations for quadratically constrained quadratic programs (2013) (0)
Approximation of global optimal values of nonconvex programs using Successive Convex Relaxation Method (Continuous and Discrete Mathematics for Optimization) (1999) (0)
Equivalent Sufficient Conditions for Global Optimality of Quadratically Constrained Quadratic Program (2023) (0)
Computational Aspects of Bilinear Matrix Inequality Problems (1998) (0)
CMPS c : A C ontinuation M ethod for P olynomial S ystems ( C + + version ) (2002) (0)
Globally Univalent C1-Maps with Separability. (1978) (0)
Monotonicity of Primal-dual Interior-point Algorithms for Semidenite Programming Problems Classication: Mathematical Programming (1998) (0)
CMPS m : A C ontinuation M ethod for P olynomial S ystems ( MATLAB version ) — User ’ s Manual (2002) (0)
Methods and apparatus for image-based communication (2006) (0)
Recognizing Underlying Sparsity in Optimization B-428 Recognizing Underlying Sparsity in Optimization (2006) (0)
A Conjugate Direction Method for Approximating the Analytic Center of a Polytope (1998) (0)
Research Reports on Mathematical and Computing Sciences Department of Mathematical and Computing Sciences Tokyo Institute of Technology SERIES B : Operations Research (2004) (0)
Solving polynomial least square problems as polynomial semidefinite programs (2008) (0)
SDP relaxations for sparse Polynomial Optimization Problems (Decision Theory and Optimization Algorithms) (2005) (0)
PARALLEL IMPLEMENTATION OF POLYHEDRAL CONTINUATION METHODS FOR SYSTEMS OF POLYNOMIAL EQUATIONS (2002) (0)
Solving Sparse Semidefinite Programs by Matrix Completion (Part II) (Mathematical Science of Optimization) (2000) (0)
B-422 Dynamic Enumeration of All Mixed Cells (2006) (0)
Semidefinite Programming Relaxation for Nonconvex Quadratic Programs(Discrete and Continuous Structures in Optimization) (1996) (0)
Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures (2020) (0)
Basic analysis of the UIP method (1991) (0)
A class of potential reduction algorithms (1991) (0)
Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems (2018) (0)
in Polyhedral Homotopy Continuation Methods (2003) (0)
2-F-7 Exploiting Equality Constraints in Sum of Squares Relaxations for Polynomial Optimization Problems(General Session(4)) (2005) (0)
B-447 Exploiting Sparsity in SDP Relaxation for Sensor Network Localization (2008) (0)
1 NUMERICAL EVALUATION OF SDPA ( SEMIDEFINITE PROGRAMMING ALGORITHM ) (2002) (0)
Nonlinear Monotone Complementarity Problems in Symmetric Matrices (1995) (0)
Computational Prospects on Copositive Programming (0)
The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint (2022) (0)
CHAPTER 2 A Primal-Dual Interior Point Algorithm for Linear Programming (2011) (0)
Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization (2012) (0)
Some Communication Problems of Two Cases in a Suckling Hospital (1992) (0)
The class of linear complementarity problems with P 0-matrices (1991) (0)
Initial points and stopping criteria (1991) (0)
Proofs of convergence theorems (1991) (0)
A robust Lagrangian-DNN method for a class of quadratic optimization problems (2016) (0)
Generating Cutting Inequalities Successively for Quadratic Optimization Problems in Binary Variables (2021) (0)
Moderate Nonconvexity = Convexity + Quadratic Concavity (Continuous and Discrete Mathematics for Optimization) (1999) (0)

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What Schools Are Affiliated With Masakazu Kojima?

Masakazu Kojima is affiliated with the following schools:

Chuo University