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Volumn 18, Issue 1, 1997, Pages 191-222

Stability of augmented system factorizations in interior-point methods

Author keywords

Interior point methods; Symmetric indefinite matrices

Indexed keywords


EID: 0031538723     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894271093     Document Type: Article
Times cited : (93)

References (25)
  • 2
    • 84966228742 scopus 로고
    • Some stable methods for calculating inertia and solving symmetric linear systems
    • J. BUNCH AND L. KAUFMAN, Some stable methods for calculating inertia and solving symmetric linear systems, Math. Comput., 31 (1977), pp. 163-179.
    • (1977) Math. Comput. , vol.31 , pp. 163-179
    • Bunch, J.1    Kaufman, L.2
  • 3
    • 0043015970 scopus 로고
    • The solution of augmented systems
    • Rutherford Appleton Laboratory, Oxon, U. K.
    • I. S. DUFF, The Solution of Augmented Systems, Technical report RAL-93-084, Rutherford Appleton Laboratory, Oxon, U. K., 1993.
    • (1993) Technical Report RAL-93-084
    • Duff, I.S.1
  • 5
    • 0002189178 scopus 로고
    • Solving symmetric indefinite systems in an interior-point method for linear programming
    • R. FOURER AND S. MEHROTRA, Solving symmetric indefinite systems in an interior-point method for linear programming, Math. Programming, 62 (1993), pp. 15-39.
    • (1993) Math. Programming , vol.62 , pp. 15-39
    • Fourer, R.1    Mehrotra, S.2
  • 6
    • 0001856557 scopus 로고
    • Theory of linear programming
    • H. W. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, NJ
    • A. J. GOLDMAN AND A. W. TUCKER, Theory of linear programming, in Linear Equalities and Related Systems, H. W. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, NJ, 1956, pp. 53-97.
    • (1956) Linear Equalities and Related Systems , pp. 53-97
    • Goldman, A.J.1    Tucker, A.W.2
  • 7
    • 0026876871 scopus 로고
    • Path-following methods in linear programming
    • C. GONZAGA, Path-following methods in linear programming, SIAM Rev., 34 (1991), pp. 167-224.
    • (1991) SIAM Rev. , vol.34 , pp. 167-224
    • Gonzaga, C.1
  • 8
    • 0001114822 scopus 로고
    • Convergence behavior of interior-point algorithms
    • O. GÜLER AND Y. YE, Convergence behavior of interior-point algorithms, Math. Programming, 60 (1993), pp. 215-228.
    • (1993) Math. Programming , vol.60 , pp. 215-228
    • Güler, O.1    Ye, Y.2
  • 9
    • 0026171528 scopus 로고
    • An O(√nL) iteration potential reduction algorithm for linear complementarity problems
    • M. KOJIMA, S. MIZUNO, AND A. YOSHISE, An O(√nL) iteration potential reduction algorithm for linear complementarity problems, Math. Programming, 50 (1991), pp. 331-342.
    • (1991) Math. Programming , vol.50 , pp. 331-342
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 10
    • 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
  • 11
    • 0028479748 scopus 로고
    • Computational experience with a globally convergent primal-dual predictor-corrector algorithm for linear programming
    • I. J. LUSTIG, R. E. MARSTEN, AND D. F. SHANNO, Computational experience with a globally convergent primal-dual predictor-corrector algorithm for linear programming, Math. Programming, 66 (1994), pp. 123-135.
    • (1994) Math. Programming , vol.66 , pp. 123-135
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 12
    • 0001662422 scopus 로고
    • Interior-point methods for linear programming: Computational state of the art
    • I. J. LUSTIG, R. E. MARSTEN, AND D. F. SHANNO, Interior-point methods for linear programming: Computational state of the art, ORSA J. Comput., 6 (1994), pp. 1-14.
    • (1994) ORSA J. Comput. , vol.6 , pp. 1-14
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 13
    • 0026386708 scopus 로고
    • On finding primal- and dual-optimal bases
    • N. MEGIDDO, On finding primal- and dual-optimal bases, ORSA J. Comput., 3 (1991), pp. 63-65.
    • (1991) ORSA J. Comput. , vol.3 , pp. 63-65
    • Megiddo, N.1
  • 14
    • 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
  • 15
    • 0000836925 scopus 로고
    • On adaptive step primal-dual interior-point algorithms for linear programming
    • S. MIZUNO, M. TODD, AND Y. YE, On adaptive step primal-dual interior-point algorithms for linear programming, Math. Oper. Res., 18 (1993), pp. 964-981.
    • (1993) Math. Oper. Res. , vol.18 , pp. 964-981
    • Mizuno, S.1    Todd, M.2    Ye, Y.3
  • 17
    • 0039606805 scopus 로고
    • Potential reduction methods in mathematical programming
    • Cornell University, Ithaca, NY
    • M. TODD, Potential Reduction Methods in Mathematical Programming, Technical report 1112, Cornell University, Ithaca, NY, 1995.
    • (1995) Technical Report , vol.1112
    • Todd, M.1
  • 18
    • 0003664630 scopus 로고
    • LOQO user's manual
    • Program in Statistics and Operations Research, Princeton University, Princeton, NJ
    • R. J. VANDERBEI, LOQO User's Manual, Technical report SOR 92-5, Program in Statistics and Operations Research, Princeton University, Princeton, NJ, 1992.
    • (1992) Technical Report SOR 92-5
    • Vanderbei, R.J.1
  • 19
    • 21844522941 scopus 로고
    • Stable numerical algorithms for equilibrium systems
    • S. VAVASIS, Stable numerical algorithms for equilibrium systems, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1108-1131.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1108-1131
    • Vavasis, S.1
  • 20
    • 0027903976 scopus 로고
    • A path-following infeasible-interior-point algorithm for linear complementarity problems
    • S. J. WRIGHT, A path-following infeasible-interior-point algorithm for linear complementarity problems, Optimization Methods Software, 2 (1993), pp. 79-106.
    • (1993) Optimization Methods Software , vol.2 , pp. 79-106
    • Wright, S.J.1
  • 21
    • 21344446747 scopus 로고    scopus 로고
    • A path-following interior-point algorithm for linear and quadratic optimization problems
    • S. J. WRIGHT, A path-following interior-point algorithm for linear and quadratic optimization problems, Ann. Oper. Res., 62 (1996), pp. 103-130.
    • (1996) Ann. Oper. Res. , vol.62 , pp. 103-130
    • Wright, S.J.1
  • 22
    • 0039014262 scopus 로고
    • Stability of linear equations solvers in interior-point methods
    • S. J. WRIGHT, Stability of linear equations solvers in interior-point methods, SIAM J. Matrix Anal. Appl., 16 (1994), pp. 1287-1307.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1287-1307
    • Wright, S.J.1
  • 23
    • 21344457406 scopus 로고    scopus 로고
    • A simplified homogeneous and self-dual linear programming algorithm and its implementation
    • X. XU, P. HUNG, AND Y. YE, A simplified homogeneous and self-dual linear programming algorithm and its implementation, Ann. Oper. Res., 62 (1996), pp. 151-172.
    • (1996) Ann. Oper. Res. , vol.62 , pp. 151-172
    • Xu, X.1    Hung, P.2    Ye, Y.3
  • 24
    • 30244459714 scopus 로고
    • On the finite convergence of interior-point algorithms for linear programming
    • Y. YE, On the finite convergence of interior-point algorithms for linear programming, Math. Programming, 57 (1992), pp. 325-336.
    • (1992) Math. Programming , vol.57 , pp. 325-336
    • Ye, Y.1
  • 25
    • 0000252459 scopus 로고
    • On the convergence of a class of infeasible-interior-point methods for the horizontal linear complementarity problem
    • Y. ZHANG, On the convergence of a class of infeasible-interior-point methods for the horizontal linear complementarity problem, SIAM J. Optim., 4 (1994), pp. 208-227.
    • (1994) SIAM J. Optim. , vol.4 , pp. 208-227
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.