Masakazu Kojima
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Mathematics
Masakazu Kojima's Degrees
- PhD Mathematics Kyoto University
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(Suggest an Edit or Addition)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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