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Volumn 30, Issue 1, 2008, Pages 223-235

On numerical issues of interior point methods

Author keywords

Indefinite Cholesky factorization; Interior point methods; Regularization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LARGE SCALE SYSTEMS; LINEARIZATION;

EID: 61849122332     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050633354     Document Type: Article
Times cited : (11)

References (27)
  • 1
    • 61849128878 scopus 로고    scopus 로고
    • E. D. ANDERSEN, J. GONDZIO, C. MÉSZÁ ROS, AND X. XU, Implementation of interior point methods for large scale linear programs, in Interior Point Methods of Mathematical Programming, T. Terlaky, ed., Appl. Math. Optim. 33, Kluwer Acad. Publ., 1996, pp. 189-252.
    • E. D. ANDERSEN, J. GONDZIO, C. MÉSZÁ ROS, AND X. XU, Implementation of interior point methods for large scale linear programs, in Interior Point Methods of Mathematical Programming, T. Terlaky, ed., Appl. Math. Optim. 33, Kluwer Acad. Publ., 1996, pp. 189-252.
  • 2
    • 0001351705 scopus 로고
    • On the augmented system approach to sparse least-squares problems
    • M. ARIOLI, I. S. DUFF, AND P. P. M. DE RIJK, On the augmented system approach to sparse least-squares problems, Numer. Math., 55 (1989), pp. 667-684.
    • (1989) Numer. Math , vol.55 , pp. 667-684
    • ARIOLI, M.1    DUFF, I.S.2    DE RIJK, P.P.M.3
  • 3
    • 0002961792 scopus 로고
    • Iterative refinement of linear least squares solutions
    • A. BJORK, Iterative refinement of linear least squares solutions, BIT, 8 (1967), pp. 8-30.
    • (1967) BIT , vol.8 , pp. 8-30
    • BJORK, A.1
  • 5
    • 0002850880 scopus 로고
    • Electronic mail distribution of linear programming test problems
    • D. M. GAY, Electronic mail distribution of linear programming test problems, COAL Newsletter, 13 (1985), pp. 10-12.
    • (1985) COAL Newsletter , vol.13 , pp. 10-12
    • GAY, D.M.1
  • 6
    • 0030532067 scopus 로고    scopus 로고
    • On the stability of Cholesky factorization for symmetric quasi-definite systems
    • P. E. GILL, M. A. SAUNDERS, AND J. R. SHINNERL, On the stability of Cholesky factorization for symmetric quasi-definite systems, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 35-46.
    • (1996) SIAM J. Matrix Anal. Appl , vol.17 , pp. 35-46
    • GILL, P.E.1    SAUNDERS, M.A.2    SHINNERL, J.R.3
  • 7
    • 0001225747 scopus 로고
    • A computational view of interior point methods for linear programming
    • J. Beasley, ed, Oxford University Press, Oxford
    • J. GONDZIO AND T. TERLAKY, A computational view of interior point methods for linear programming, in Advances in Linear and Integer Programming, J. Beasley, ed., Oxford University Press, Oxford, 1995, pp. 103-144.
    • (1995) Advances in Linear and Integer Programming , pp. 103-144
    • GONDZIO, J.1    TERLAKY, T.2
  • 9
    • 0000114112 scopus 로고
    • Computational experience with a primaldual interior point method for linear programming
    • I. J. LUSTIG, R. E. MARSTEN, AND D. F. SHANNO, Computational experience with a primaldual interior point method for linear programming, Linear Algebra Appl., 152 (1991), pp. 191-222.
    • (1991) Linear Algebra Appl , vol.152 , pp. 191-222
    • LUSTIG, I.J.1    MARSTEN, R.E.2    SHANNO, D.F.3
  • 10
    • 0032098605 scopus 로고    scopus 로고
    • The role of the augmented system in interior point methods
    • I. MAROS AND C. MÉSZÁROS, The role of the augmented system in interior point methods, Eur. J. Oper. Res., 107 (1998), pp. 720-736.
    • (1998) Eur. J. Oper. Res , vol.107 , pp. 720-736
    • MAROS, I.1    MÉSZÁROS, C.2
  • 11
    • 1642586652 scopus 로고    scopus 로고
    • A repository of convex quadratic programming problems
    • The test problems are available online from ftp://ftp.sztaki.hu/pub/oplab/QPDATA
    • I. MAROS AND C. MÉSZÁROS, A repository of convex quadratic programming problems, Optim. Methods Softw., 11/12 (1999), pp. 671-681. The test problems are available online from ftp://ftp.sztaki.hu/pub/oplab/QPDATA.
    • (1999) Optim. Methods Softw , vol.11-12 , pp. 671-681
    • MAROS, I.1    MÉSZÁROS, C.2
  • 13
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • S. MEHROTRA, On the implementation of a primal-dual interior point method, SIAM J. Optim., 2 (1992), pp. 575-601.
    • (1992) SIAM J. Optim , vol.2 , pp. 575-601
    • MEHROTRA, S.1
  • 14
    • 34250077538 scopus 로고
    • Finding an interior point in the optimal face of linear programs
    • S. MEHROTRA AND Y. YE, Finding an interior point in the optimal face of linear programs, Math. Programming, 62 (1993), pp. 497-515.
    • (1993) Math. Programming , vol.62 , pp. 497-515
    • MEHROTRA, S.1    YE, Y.2
  • 15
    • 1642635875 scopus 로고    scopus 로고
    • On free variables in interior point methods
    • C. MÉSZÁROS, On free variables in interior point methods, Optim. Methods Softw., 9 (1997), pp. 121-139.
    • (1997) Optim. Methods Softw , vol.9 , pp. 121-139
    • MÉSZÁROS, C.1
  • 16
    • 1642618002 scopus 로고    scopus 로고
    • The BPMPD interior-point solver for convex quadratic problems
    • C. MÉSZÁROS, The BPMPD interior-point solver for convex quadratic problems, Optim. Methods Softw., 11/12 (1999), pp. 431-449.
    • (1999) Optim. Methods Softw , vol.11-12 , pp. 431-449
    • MÉSZÁROS, C.1
  • 17
    • 26444592252 scopus 로고    scopus 로고
    • On the Cholesky factorization in interior point methods
    • C. MÉSZÁROS, On the Cholesky factorization in interior point methods, Comput. Math. Appl., 50 (2005), pp. 1157-1166.
    • (2005) Comput. Math. Appl , vol.50 , pp. 1157-1166
    • MÉSZÁROS, C.1
  • 18
    • 1442280698 scopus 로고    scopus 로고
    • Advanced preprocessing techniques for linear and quadratic programming
    • C. MÉSZÁROS AND U.H. SUHL, Advanced preprocessing techniques for linear and quadratic programming, OR Spectrum, 25 (2004), pp. 575-595.
    • (2004) OR Spectrum , vol.25 , pp. 575-595
    • MÉSZÁROS, C.1    SUHL, U.H.2
  • 19
    • 0039943513 scopus 로고
    • LSQR: An algorithm for sparse linear equations and leastsquares problems
    • C. C. PAIGE AND M. A. SAUNDERS, LSQR: An algorithm for sparse linear equations and leastsquares problems, ACM Trans. Math. Software, 8 (1982), pp. 43-71.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 43-71
    • PAIGE, C.C.1    SAUNDERS, M.A.2
  • 20
    • 61849135407 scopus 로고    scopus 로고
    • M. A. SAUNDERS, Major Cholesky would feel proud, ORSA J. Comput., 6 (1994), pp. 94-105.
    • M. A. SAUNDERS, Major Cholesky would feel proud, ORSA J. Comput., 6 (1994), pp. 94-105.
  • 21
    • 0000307001 scopus 로고
    • Solution of sparse rectangular systems using LSQR and CRAIG
    • M. A. SAUNDERS, Solution of sparse rectangular systems using LSQR and CRAIG, BIT, 35 (1995), pp. 588-604.
    • (1995) BIT , vol.35 , pp. 588-604
    • SAUNDERS, M.A.1
  • 22
    • 0039169750 scopus 로고    scopus 로고
    • Cholesky-based methods for sparse least squares: The benefits of regularization
    • L. Adams and J. L. Nazareth, eds, SIAM
    • M. A. SAUNDERS, Cholesky-based methods for sparse least squares: The benefits of regularization, in Linear and Nonlinear Conjugate Gradient-Related Methods, L. Adams and J. L. Nazareth, eds., SIAM, 1996, pp. 92-100.
    • (1996) Linear and Nonlinear Conjugate Gradient-Related Methods , pp. 92-100
    • SAUNDERS, M.A.1
  • 23
    • 0002090173 scopus 로고
    • Symmetric quasi-definite matrices
    • R. J. VANDERBEI, Symmetric quasi-definite matrices, SIAM J. Optim., 5 (1995), pp. 100-113.
    • (1995) SIAM J. Optim , vol.5 , pp. 100-113
    • VANDERBEI, R.J.1
  • 24
    • 0001511481 scopus 로고
    • Some properties of the Hessian of the logarithmic barrier function
    • M. H. WRIGHT, Some properties of the Hessian of the logarithmic barrier function, Math. Programming, 67 (1994), pp. 265-295.
    • (1994) Math. Programming , vol.67 , pp. 265-295
    • WRIGHT, M.H.1
  • 26
    • 0031538723 scopus 로고    scopus 로고
    • Stability of augmented system factorizations in interior-point methods
    • S. J. WRIGHT, Stability of augmented system factorizations in interior-point methods, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 191-222.
    • (1997) SIAM J. Matrix Anal. Appl , vol.18 , pp. 191-222
    • WRIGHT, S.J.1
  • 27
    • 0033432390 scopus 로고    scopus 로고
    • Modified Cholesky factorizations in interior-point algorithms for linear programming
    • S. J. WRIGHT, Modified Cholesky factorizations in interior-point algorithms for linear programming, SIAM J. Optim., 9 (1999), pp. 1159-1191.
    • (1999) SIAM J. Optim , vol.9 , pp. 1159-1191
    • WRIGHT, S.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.