All Stories

  1. Strong duality of a conic optimization problem with a single hyperplane and two cone constraints

    Article • Optimization, August 2023, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  2. Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints

    Article • Mathematical Programming, November 2020, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  3. A Newton-bracketing method for a simple conic optimization problem

    Article • Optimization Methods and Software, July 2020, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  4. Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures

    Article • Journal of Global Optimization, January 2020, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  5. A Geometrical Analysis on Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems

    Article • SIAM Journal on Optimization, January 2020, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  6. Algorithm 996

    Article • ACM Transactions on Mathematical Software, July 2019, ACM (Association for Computing Machinery)

    Prof Kim-Chuan Toh, Professor Emeritus Masakazu Kojima

  7. A robust Lagrangian-DNN method for a class of quadratic optimization problems

    Article • Computational Optimization and Applications, October 2016, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  8. Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization

    Article • Journal of Optimization Theory and Applications, August 2015, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  9. A Lagrangian–DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems

    Article • Mathematical Programming, February 2015, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  10. Faster, but weaker, relaxations for quadratically constrained quadratic programs

    Article • Computational Optimization and Applications, November 2013, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  11. A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming

    Article • SIAM Journal on Optimization, January 2013, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  12. Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

    Article • September 2011, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  13. Semidefinite programming relaxations for sensor network localization

    Article • September 2010, Institute of Electrical & Electronics Engineers (IEEE)

    Professor Emeritus Masakazu Kojima

  14. Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion

    Article • Mathematical Programming, August 2010, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  15. A numerical algorithm for block-diagonal decomposition of matrix $${*}$$ -algebras with application to semidefinite programming

    Article • Japan Journal of Industrial and Applied Mathematics, May 2010, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  16. SDP RELAXATIONS FOR QUADRATIC OPTIMIZATION PROBLEMS DERIVED FROM POLYNOMIAL OPTIMIZATION PROBLEMS

    Article • Asia-Pacific Journal of Operational Research, February 2010, World Scientific Pub Co Pte Lt

    Professor Emeritus Masakazu Kojima

  17. Solving polynomial least squares problems via semidefinite programming relaxations

    Article • Journal of Global Optimization, February 2009, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  18. Exploiting Sparsity in SDP Relaxation for Sensor Network Localization

    Article • SIAM Journal on Optimization, January 2009, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  19. Algorithm 883

    Article • ACM Transactions on Mathematical Software, July 2008, ACM (Association for Computing Machinery)

    Professor Emeritus Masakazu Kojima

  20. Recognizing underlying sparsity in optimization

    Article • Mathematical Programming, March 2008, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  21. EQUALITY BASED CONTRACTION OF SEMIDEFINITE PROGRAMMING RELAXATIONS IN POLYNOMIAL OPTIMIZATION

    Article • Journal of the Operations Research Society of Japan, January 2008, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  22. SPARSE SECOND ORDER CONE PROGRAMMING FORMULATIONS FOR CONVEX OPTIMIZATION PROBLEMS

    Article • Journal of the Operations Research Society of Japan, January 2008, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  23. Correlative Sparsity in Primal-Dual Interior-Point Methods for LP, SDP, and SOCP

    Article • Applied Mathematics & Optimization, November 2007, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  24. A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones

    Article • Computational Optimization and Applications, October 2007, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  25. Dynamic Enumeration of All Mixed Cells

    Article • Discrete & Computational Geometry, March 2007, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  26. An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones

    Article • Mathematical Programming, June 2006, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  27. Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

    Article • SIAM Journal on Optimization, January 2006, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  28. Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems

    Article • SIAM Journal on Optimization, January 2005, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  29. Sparsity in sums of squares of polynomials

    Article • Mathematical Programming, December 2004, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  30. PHoM ? a Polyhedral Homotopy Continuation Method for Polynomial Systems

    Article • Computing, March 2004, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  31. SOLVING LARGE SCALE OPTIMIZATION PROBLEMS VIA GRID AND CLUSTER COMPUTING(<Special Issue>Network Design, Control and Optimization)

    Article • Journal of the Operations Research Society of Japan, January 2004, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  32. Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint

    Article • Optimization Methods and Software, October 2003, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  33. Implementation and evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0)

    Article • Optimization Methods and Software, August 2003, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  34. Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0)

    Article • Optimization Methods and Software, August 2003, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  35. The Lagrangian Picture, Part II : Models and Applications of the Lagrangian Approach to Solute Transport

    Article • April 2003, Oxford University Press (OUP)

    Professor Emeritus Masakazu Kojima

  36. The Lagrangian Picture, Part I : Fundamentals of the Lagrangian Approach to Solute Transport

    Article • April 2003, Oxford University Press (OUP)

    Professor Emeritus Masakazu Kojima

  37. Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods

    Article • Journal of Computational and Applied Mathematics, March 2003, Elsevier

    Professor Emeritus Masakazu Kojima

  38. Exploiting sparsity in semidefinite programming via matrix completion II: implementation and numerical results

    Article • Mathematical Programming, February 2003, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  39. A GENERAL FRAMEWORK FOR CONVEX RELAXATION OF POLYNOMIAL OPTIMIZATION PROBLEMS OVER CONES

    Article • Journal of the Operations Research Society of Japan, January 2003, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  40. CMPSM: A CONTINUATION METHOD FOR POLYNOMIAL SYSTEMS (MATLAB VERSION)

    Article • July 2002, World Scientific Pub Co Pte Lt

    Professor Emeritus Masakazu Kojima

  41. PARALLEL IMPLEMENTATION OF POLYHEDRAL CONTINUATION METHODS FOR SYSTEMS OF POLYNOMIAL EQUATIONS

    Article • July 2002, World Scientific Pub Co Pte Lt

    Professor Emeritus Masakazu Kojima

  42. Lagrangian Dual Interior-Point Methods for Semidefinite Programs

    Article • SIAM Journal on Optimization, January 2002, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  43. ENUMERATION OF ALL SOLUTIONS OF A COMBINATORIAL LINEAR INEQUALITY SYSTEM ARISING FROM THE POLYHEDRAL HOMOTOPY CONTINUATION METHOD

    Article • Journal of the Operations Research Society of Japan, January 2002, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  44. Complexity Analysis of Successive Convex Relaxation Methods for Nonconvex Sets

    Article • Mathematics of Operations Research, August 2001, INFORMS

    Professor Emeritus Masakazu Kojima

  45. Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework

    Article • SIAM Journal on Optimization, January 2001, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  46. Successive Convex Relaxation Approach to Bilevel Quadratic Optimization Problems

    Article • January 2001, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  47. Numerical Evaluation of SDPA (Semidefinite Programming Algorithm)

    Article • January 2000, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  48. Towards Implementations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems

    Article • January 2000, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  49. Search directions in the SDP and the monotone SDLCP: generalization and inexact computation

    Article • Mathematical Programming, May 1999, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  50. A note on the Nesterov-Todd and the Kojima-Shindoh-hara search directions in semidefinite programming

    Article • Optimization Methods and Software, January 1999, Taylor & Francis

    Professor Emeritus Masakazu Kojima

  51. A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh--Haeberly--Overton Search Direction

    Article • SIAM Journal on Optimization, January 1999, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  52. Existence and Uniqueness of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP

    Article • SIAM Journal on Optimization, May 1998, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  53. Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs

    Article • Mathematical Programming, January 1998, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  54. A conjugate direction method for approximating the analytic center of a polytope

    Article • Journal of Inequalities and Applications, January 1998, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  55. Centers of Monotone Generalized Complementarity Problems

    Article • Mathematics of Operations Research, November 1997, INFORMS

    Professor Emeritus Masakazu Kojima

  56. Exploiting sparsity in primal-dual interior-point methods for semidefinite programming

    Article • Mathematical Programming, October 1997, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  57. Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming

    Article • SIAM Journal on Optimization, February 1995, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  58. Global convergence in infeasible-interior-point algorithms

    Article • Mathematical Programming, February 1994, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  59. A General Framework of Continuation Methods for Complementarity Problems

    Article • Mathematics of Operations Research, November 1993, INFORMS

    Professor Emeritus Masakazu Kojima

  60. A primal—dual infeasible-interior-point algorithm for linear programming

    Article • Mathematical Programming, August 1993, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  61. Large-Step Interior Point Algorithms for Linear Complementarity Problems

    Article • SIAM Journal on Optimization, May 1993, Society for Industrial & Applied Mathematics (SIAM)

    Professor Emeritus Masakazu Kojima

  62. A little theorem of the bigℳ in interior point algorithms

    Article • Mathematical Programming, March 1993, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  63. Theoretical convergence of large-step primal—dual interior point algorithms for linear programming

    Article • Mathematical Programming, March 1993, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  64. An interior point potential reduction algorithm for the linear complementarity problem

    Article • Mathematical Programming, February 1992, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  65. Homotopy Continuation Methods for Nonlinear Complementarity Problems

    Article • Mathematics of Operations Research, November 1991, INFORMS

    Professor Emeritus Masakazu Kojima

  66. A unified approach to interior point algorithms for linear complementarity problems: A summary

    Article • Operations Research Letters, July 1991, Elsevier

    Professor Emeritus Masakazu Kojima

  67. The relation between the path of centers and Smale's regularization of the linear programming problem

    Article • Linear Algebra and its Applications, July 1991, Elsevier

    Professor Emeritus Masakazu Kojima

  68. An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems

    Article • Mathematical Programming, March 1991, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  69. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems

    Article • January 1991, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  70. Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems

    Article • Mathematics of Operations Research, November 1990, INFORMS

    Professor Emeritus Masakazu Kojima

  71. Ellipsoids that contain all the solutions of a positive semi-definite linear complementarity problem

    Article • Mathematical Programming, March 1990, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  72. A polynomial-time algorithm for a class of linear complementarity problems

    Article • Mathematical Programming, May 1989, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  73. A Primal-Dual Interior Point Algorithm for Linear Programming

    Article • January 1989, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  74. A new continuation method for complementarity problems with uniformP-functions

    Article • Mathematical Programming, January 1989, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  75. Determining basic variables of optimal solutions in Karmarkar's new LP algorithm

    Article • Algorithmica, November 1986, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  76. EXTENSION OF NEWTON AND QUASI-NEWTON METHODS TO SYSTEMS OF PC^1 EQUATIONS

    Article • Journal of the Operations Research Society of Japan, January 1986, The Operations Research Society of Japan

    Professor Emeritus Masakazu Kojima

  77. Strongly Stable Equilibrium Points of N-Person Noncooperative Games

    Article • Mathematics of Operations Research, November 1985, INFORMS

    Professor Emeritus Masakazu Kojima

  78. A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm

    Article • Mathematical Programming, October 1984, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  79. Continuous deformation of nonlinear programs

    Article • January 1984, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  80. Computation of all solutions to a system of polynomial equations

    Article • Mathematical Programming, June 1983, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  81. Strongly Stable Stationary Solutions in Nonlinear Programs

    Article • January 1980, Elsevier

    Professor Emeritus Masakazu Kojima

  82. A PL homotopy for finding all the roots of a polynomial

    Article • Mathematical Programming, December 1979, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  83. A modification of todd's triangulationJ 3

    Article • Mathematical Programming, December 1978, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  84. On the homotopic approach to systems of equations with separable mappings

    Article • January 1978, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima

  85. On the existence and uniqueness of solutions in nonlinear complementarity theory

    Article • Mathematical Programming, December 1977, Springer Science + Business Media

    Professor Emeritus Masakazu Kojima