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Volumn 8, Issue 4, 1998, Pages 916-939

Curvilinear stabilization techniques for truncated Newton methods in large scale unconstrained optimization

Author keywords

Curvilinear linesearch; Lanczos method; Large scale unconstrained optimization; Negative curvature direction; Newton type method

Indexed keywords


EID: 0032327057     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495295250     Document Type: Article
Times cited : (43)

References (29)
  • 2
  • 6
    • 0020763823 scopus 로고
    • Truncated-Newton methods algorithms for large-scale unconstrained optimization
    • R. DEMBO AND T. STEIHAUG, Truncated-Newton methods algorithms for large-scale unconstrained optimization, Math. Programming, 26 (1983), pp. 190-212.
    • (1983) Math. Programming , vol.26 , pp. 190-212
    • Dembo, R.1    Steihaug, T.2
  • 7
    • 0027544412 scopus 로고
    • Nonmonotonic trust region algorithm
    • N. DENG, Y. XIAO, AND F. ZHOU, Nonmonotonic trust region algorithm, J. Optim. Theory Appl., 76 (1993), pp. 259-285.
    • (1993) J. Optim. Theory Appl. , vol.76 , pp. 259-285
    • Deng, N.1    Xiao, Y.2    Zhou, F.3
  • 8
    • 0030243966 scopus 로고    scopus 로고
    • Nonmonotone curvilinear linesearch methods for unconstrained optimization
    • M. FERRIS, S. LUCIDI, AND M. ROMA, Nonmonotone curvilinear linesearch methods for unconstrained optimization, Comput. Optim. Appl., 6 (1996), pp. 117-136.
    • (1996) Comput. Optim. Appl. , vol.6 , pp. 117-136
    • Ferris, M.1    Lucidi, S.2    Roma, M.3
  • 11
    • 0022766519 scopus 로고
    • A nonmonotone line search technique for Newton's method
    • L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal., 23 (1986), pp. 707-716.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 707-716
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 12
    • 0000843862 scopus 로고
    • A truncated Newton method with nonmonotone linesearch for unconstrained optimization
    • L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A truncated Newton method with nonmonotone linesearch for unconstrained optimization, J. Optim. Theory Appl., 60 (1989), pp. 401-419.
    • (1989) J. Optim. Theory Appl. , vol.60 , pp. 401-419
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 13
    • 0001028609 scopus 로고
    • A class of nonmonotone stabilization methods in unconstrained optimization
    • L. GRIPPO, F. LAMPARIELLO, AND S. LUCIDI, A class of nonmonotone stabilization methods in unconstrained optimization, Numer. Math., 59 (1991), pp. 779-805.
    • (1991) Numer. Math. , vol.59 , pp. 779-805
    • Grippo, L.1    Lampariello, F.2    Lucidi, S.3
  • 15
    • 0000149118 scopus 로고
    • A modification of Armijo's step-size rule for negative curvature
    • G. MCCORMICK, A modification of Armijo's step-size rule for negative curvature, Math. Programming, 13 (1977), pp. 111-115.
    • (1977) Math. Programming , vol.13 , pp. 111-115
    • Mccormick, G.1
  • 17
    • 0001818862 scopus 로고
    • On the use of directions of negative curvature in a modified Newton method
    • J. MORÉ AND D. SORENSEN, On the use of directions of negative curvature in a modified Newton method, Math. Programming, 16 (1979), pp. 1-20.
    • (1979) Math. Programming , vol.16 , pp. 1-20
    • Moré, J.1    Sorensen, D.2
  • 18
    • 0021481124 scopus 로고
    • Newton-type minimization via the Lanczos method
    • S. G. NASH, Newton-type minimization via the Lanczos method, SIAM J. Numer. Anal., 21 (1984), pp. 770-788.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 770-788
    • Nash, S.G.1
  • 19
    • 0001585735 scopus 로고
    • Preconditioning of truncated-Newton methods
    • S. G. NASH, Preconditioning of truncated-Newton methods, SIAM J. Sci. Stat. Comput., 6 (1985), pp. 599-616.
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 599-616
    • Nash, S.G.1
  • 21
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • C. C. PAIGE AND M. A. SAUNDERS, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal., 12 (1975), pp. 617-629.
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 22
    • 0003668665 scopus 로고
    • Prentice-Hall Series in Computational Mathematics, Prentice-Hall, Englewood Cliffs, NJ
    • B. PARLETT, The Symmetric Eigenvalue Problem, Prentice-Hall Series in Computational Mathematics, Prentice-Hall, Englewood Cliffs, NJ, 1980.
    • (1980) The Symmetric Eigenvalue Problem
    • Parlett, B.1
  • 23
    • 0026824139 scopus 로고
    • TNPACK - A truncated Newton package for large-scale problems: I. Algorithm and usage
    • T. SCHLICK AND A. FOGELSON, TNPACK - A truncated Newton package for large-scale problems: I. Algorithm and usage, ACM Trans. Math. Software, 18 (1992), pp. 46-70.
    • (1992) ACM Trans. Math. Software , vol.18 , pp. 46-70
    • Schlick, T.1    Fogelson, A.2
  • 24
    • 0022015590 scopus 로고
    • A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties
    • G. A. SHULTZ, R. B. SCHNABEL, AND R. H. BYRD, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties, SIAM J. Numer. Anal., 22 (1985), pp. 47-67.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 47-67
    • Shultz, G.A.1    Schnabel, R.B.2    Byrd, R.H.3
  • 25
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a k-step Arnoldi method
    • D. C. SORENSEN, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 357-385.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 357-385
    • Sorensen, D.C.1
  • 26
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • I. S. Duff, ed., Academic Press, London
    • P. TOINT, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57-88.
    • (1981) Sparse Matrices and Their Uses , pp. 57-88
    • Toint, P.1
  • 27
    • 0001019976 scopus 로고    scopus 로고
    • An assessment of nonmonotone linesearch techniques for unconstrained optimization
    • P. L. TOINT, An assessment of nonmonotone linesearch techniques for unconstrained optimization, SIAM J. Sci. Comput., 17 (1996), pp. 725-739.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 725-739
    • Toint, P.L.1
  • 28
    • 0001898672 scopus 로고    scopus 로고
    • Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints
    • P. TOINT, Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints, Math. Programming, 77 (1997), pp. 69-94.
    • (1997) Math. Programming , vol.77 , pp. 69-94
    • Toint, P.1
  • 29
    • 0038821467 scopus 로고
    • Nonmonotone trust region methods with curvilinear path in unconstrained minimization
    • Y. XIAO AND F. ZHOU, Nonmonotone trust region methods with curvilinear path in unconstrained minimization, Computing, 48 (1992), pp. 303-317.
    • (1992) Computing , vol.48 , pp. 303-317
    • Xiao, Y.1    Zhou, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.