메뉴 건너뛰기




Volumn 103, Issue 1, 2005, Pages 153-179

Product-form Cholesky factorization in interior point methods for second-order cone programming

Author keywords

Interior point methods; Product form Cholesky factorization; Second order cone programming

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

EID: 17444398132     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-004-0556-1     Document Type: Article
Times cited : (18)

References (31)
  • 2
    • 0003654728 scopus 로고    scopus 로고
    • Optimization with semidefinite, quadratic and linear constraints
    • RUTCOR, Rutgers University, NJ
    • Alizadeh, F., Schmieta, S.: Optimization with semidefinite, quadratic and linear constraints. Technical Report, RUTCOR, Rutgers University, NJ, 1997
    • (1997) Technical Report
    • Alizadeh, F.1    Schmieta, S.2
  • 3
    • 0003832298 scopus 로고    scopus 로고
    • On implementing a primal-dual interior-point method for conic quadratic optimization. Helsinki School of Economics and Business Administration
    • Andersen, E., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Helsinki School of Economics and Business Administration, Working paper W-274, 2000
    • (2000) Working Paper , vol.W-274
    • Andersen, E.1    Roos, C.2    Terlaky, T.3
  • 4
    • 0030247572 scopus 로고    scopus 로고
    • A modified Schur complement method for handling dense columns in interior point methods for linear programming
    • Andersen, K.D.: A modified Schur complement method for handling dense columns in interior point methods for linear programming. ACM Transactions on Mathematical Software, 22 (3), 348-356 (1996)
    • (1996) ACM Transactions on Mathematical Software , vol.22 , Issue.3 , pp. 348-356
    • Andersen, K.D.1
  • 5
    • 0001612957 scopus 로고
    • Triangular factors of modified matrices
    • Bennett, J.M.: Triangular factors of modified matrices. Numerisches Mathematik 7, 217-221 (1965)
    • (1965) Numerisches Mathematik , vol.7 , pp. 217-221
    • Bennett, J.M.1
  • 6
    • 0041603476 scopus 로고
    • Further development of primal-dual interior point methods
    • Choi, I.C., Monma, C.L., Shanno, D.F.: Further development of primal-dual interior point methods. ORSA J. Comput. 2 (4), 304-311 (1990)
    • (1990) ORSA J. Comput. , vol.2 , Issue.4 , pp. 304-311
    • Choi, I.C.1    Monma, C.L.2    Shanno, D.F.3
  • 8
    • 0000847769 scopus 로고
    • Least squares computations by Givens transformations without square roots
    • Gentleman, W.M.: Least squares computations by Givens transformations without square roots. J. Inst. Math. Appl. 12, 329-336 (1973)
    • (1973) J. Inst. Math. Appl. , vol.12 , pp. 329-336
    • Gentleman, W.M.1
  • 9
    • 84966213048 scopus 로고
    • Methods for computing and modifying the LDV factors of a matrix
    • Gill, Ph.E., Murray, W., Saunders, M.A.: Methods for computing and modifying the LDV factors of a matrix. Math. Comput. 29, 1051-10 (1975)
    • (1975) Math. Comput. , vol.29 , pp. 1051-1110
    • Gill, Ph.E.1    Murray, W.2    Saunders, M.A.3
  • 10
    • 17444402222 scopus 로고    scopus 로고
    • The conic simplex method
    • IEOR Dept. Columbia University, New York, NY
    • Goldfarb, D.: The conic simplex method. CORC Report, IEOR Dept. Columbia University, New York, NY, 2002
    • (2002) CORC Report
    • Goldfarb, D.1
  • 11
    • 17444363113 scopus 로고    scopus 로고
    • A product-form Cholesky factorization method for handling dense columns in interior point methods for linear programming
    • Goldfarb, D., Scheinberg, K.: A product-form Cholesky factorization method for handling dense columns in interior point methods for linear programming. Mathematical Programming, 99, 1-34 (2004)
    • (2004) Mathematical Programming , vol.99 , pp. 1-34
    • Goldfarb, D.1    Scheinberg, K.2
  • 14
    • 0002431411 scopus 로고
    • An implementation of a primal-dual method for linear programming
    • McShane, K.A., Monma, C.L., Shanno, D.F.: An implementation of a primal-dual method for linear programming. ORSA J. Comput. 1 (2), 70-83 (1989)
    • (1989) ORSA J. Comput. , vol.1 , Issue.2 , pp. 70-83
    • McShane, K.A.1    Monma, C.L.2    Shanno, D.F.3
  • 17
    • 0032345991 scopus 로고    scopus 로고
    • Superlinear convergence of a symmetric primal-dual path following algorithms for semidefinite programming
    • Luo, Z.-Q., Sturm, J., Zhang, S.: Superlinear convergence of a symmetric primal-dual path following algorithms for semidefinite programming. SIAM J. Optimization 8 (1), 59-81 (1998)
    • (1998) SIAM J. Optimization , vol.8 , Issue.1 , pp. 59-81
    • Luo, Z.-Q.1    Sturm, J.2    Zhang, S.3
  • 18
    • 0031285899 scopus 로고    scopus 로고
    • Primal-dual path-following algorithms for semidefinite programming
    • Monteiro, R.D.C.: Primal-dual path-following algorithms for semidefinite programming. SIAM J. Optimization 7, 663-678 (1997)
    • (1997) SIAM J. Optimization , vol.7 , pp. 663-678
    • Monteiro, R.D.C.1
  • 19
    • 0000809108 scopus 로고    scopus 로고
    • Extension of Karmarkar's algorithm to convex quadratically constrained quadratic problems
    • Nemirovskii, A.S., Scheinberg, K.: Extension of Karmarkar's algorithm to convex quadratically constrained quadratic problems. Mathematical Programming 72, 273-289 (1996)
    • (1996) Mathematical Programming , vol.72 , pp. 273-289
    • Nemirovskii, A.S.1    Scheinberg, K.2
  • 21
    • 0031073753 scopus 로고    scopus 로고
    • Self-scaled barriers and interior-point methods for convex programming
    • Nesterov, Yu.E., Todd, M.J.: Self-Scaled Barriers and Interior-Point Methods for Convex Programming. Math. Oper. Res. 22, 1-42 (1997)
    • (1997) Math. Oper. Res. , vol.22 , pp. 1-42
    • Nesterov, Yu.E.1    Todd, M.J.2
  • 22
    • 0032222088 scopus 로고    scopus 로고
    • Primal-dual interior-point methods for self-scaled cones
    • Nesterov, Yu.E., Todd, M.J.: Primal-Dual Interior-Point Methods for Self-Scaled Cones. SIAM J. Optimization 8, 324-364 (1998)
    • (1998) SIAM J. Optimization , vol.8 , pp. 324-364
    • Nesterov, Yu.E.1    Todd, M.J.2
  • 23
    • 17444362754 scopus 로고    scopus 로고
    • Pataki, G., Schmieta, S.: http://dimacs.rutgers.edu/Challenges/Seventh/ Instances, 1999
    • (1999)
    • Pataki, G.1    Schmieta, S.2
  • 24
    • 17444380202 scopus 로고    scopus 로고
    • Notes on modified Cholesky factorizations and Schur complements for linear systems from interior point methods
    • Scheinberg, K., Wright, S.: Notes on modified Cholesky factorizations and Schur complements for linear systems from interior point methods. Working paper, 1998
    • (1998) Working Paper
    • Scheinberg, K.1    Wright, S.2
  • 25
    • 0035435165 scopus 로고    scopus 로고
    • Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones
    • Schmieta, S.H., Alizadeh, F.: Associative and Jordan algebras, and polynomial time interior-point algorithms for symmetric cones. Math. O.R. 26 (3), 543-564 (2001)
    • (2001) Math. O.R. , vol.26 , Issue.3 , pp. 543-564
    • Schmieta, S.H.1    Alizadeh, F.2
  • 26
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11-12, 625-653 (1999)
    • (1999) Optimization Methods and Software , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 27
    • 17444404688 scopus 로고    scopus 로고
    • Avoiding numerical cancellation in the interior point method for solving semidefinite programs
    • Sturm, J.F.: Avoiding numerical cancellation in the interior point method for solving semidefinite programs. Mathematical Programming, Series B 95 (2), 219-247 (2003)
    • (2003) Mathematical Programming, Series B , vol.95 , Issue.2 , pp. 219-247
    • Sturm, J.F.1
  • 28
    • 0003843753 scopus 로고    scopus 로고
    • A polynomial primal-dual path-following algorithm for second-order cone programming
    • The Institute of Statistical Mathematics, Tokyo, Japan
    • Tsuchiya, T.: A Polynomial Primal-Dual Path-Following Algorithm for Second-Order Cone Programming. Technical Report Research Memorandum No. 649, The Institute of Statistical Mathematics, Tokyo, Japan, 1997
    • (1997) Technical Report Research Memorandum No. 649 , vol.649
    • Tsuchiya, T.1
  • 30
    • 0033432390 scopus 로고    scopus 로고
    • Modified Cholesky factorizations in interior point algorithms for linear programming
    • Wright, S. J.: Modified Cholesky factorizations in interior point algorithms for linear programming. SIAM J. Optimization 9 (4), 1159-1191 (1999)
    • (1999) SIAM J. Optimization , vol.9 , Issue.4 , pp. 1159-1191
    • Wright, S.J.1
  • 31
    • 0032081158 scopus 로고    scopus 로고
    • On extending primal-dual interior-point algorithms from linear programming to semidefinite programming
    • Zhang, Y.: On extending primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM J. Optimization 8, 356-386 (1998)
    • (1998) SIAM J. Optimization , vol.8 , pp. 356-386
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.