메뉴 건너뛰기




Volumn 34, Issue 1, 2003, Pages 85-102

Gauss quadrature applied to trust region computations

Author keywords

Bounds; Lanczos process; Optimization; Quasi Newton method

Indexed keywords


EID: 0346463241     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026130310913     Document Type: Article
Times cited : (7)

References (19)
  • 1
    • 0000924088 scopus 로고    scopus 로고
    • Estimation of the L-curve via Lanczos bidiagonalization
    • D. Calvetti, G.H. Golub and L. Reichel, Estimation of the L-curve via Lanczos bidiagonalization, BIT 39 (1999) 603-619.
    • (1999) BIT , vol.39 , pp. 603-619
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 4
    • 0000955796 scopus 로고
    • Computing optimal locally constrained steps
    • D.M. Gay, Computing optimal locally constrained steps, SIAM J. Sci. Statist. Comput. 2 (1981) 186-197.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 5
    • 0003093333 scopus 로고
    • Matrices, moments and quadrature
    • eds. D.F. Griffiths and G.A. Watson (Longman, Essex)
    • G.H. Golub and G. Meurant, Matrices, moments and quadrature, in: Numerical Analysis 1993, eds. D.F. Griffiths and G.A. Watson (Longman, Essex, 1994) pp. 105-156.
    • (1994) Numerical Analysis 1993 , pp. 105-156
    • Golub, G.H.1    Meurant, G.2
  • 7
    • 0001678475 scopus 로고
    • Quadratically constrained least squares and quadratic problems
    • G.H. Golub and U. von Matt, Quadratically constrained least squares and quadratic problems, Numer. Math. 59 (1991) 561-580.
    • (1991) Numer. Math. , vol.59 , pp. 561-580
    • Golub, G.H.1    Von Matt, U.2
  • 8
    • 0033437435 scopus 로고    scopus 로고
    • Solving the trust-region subproblem using the Lanczos method
    • N.I.M. Gould, S. Lucidi, M. Roma and P.L. Toint, Solving the trust-region subproblem using the Lanczos method, SIAM J. Optim. 9 (1999) 504-525.
    • (1999) SIAM J. Optim. , vol.9 , pp. 504-525
    • Gould, N.I.M.1    Lucidi, S.2    Roma, M.3    Toint, P.L.4
  • 9
    • 0036347958 scopus 로고    scopus 로고
    • Minimizing a quadratic over a sphere
    • W.W. Hager, Minimizing a quadratic over a sphere, SIAM J. Optim. 12 (2001) 188-208.
    • (2001) SIAM J. Optim. , vol.12 , pp. 188-208
    • Hager, W.W.1
  • 10
    • 0346113871 scopus 로고    scopus 로고
    • A note on Tikhonov regularization of large linear problems
    • to appear
    • M. Hanke, A note on Tikhonov regularization of large linear problems, BIT, to appear.
    • BIT
    • Hanke, M.1
  • 12
    • 0003162836 scopus 로고
    • Recent developments in algorithms and software for trust region methods
    • eds. A. Bachem, M. Grötschel and B. Korte (Springer, Berlin)
    • J. J. Moré, Recent developments in algorithms and software for trust region methods, in: Mathematical Programming: The State of the Art, eds. A. Bachem, M. Grötschel and B. Korte (Springer, Berlin, 1983) pp. 258-287.
    • (1983) Mathematical Programming: The State of the Art , pp. 258-287
    • Moré, J.J.1
  • 15
    • 18044401847 scopus 로고    scopus 로고
    • A new matrix-free algorithm for the large-scale trust-region subproblem
    • M. Rojas, S.A. Santos and D.C. Sorensen, A new matrix-free algorithm for the large-scale trust-region subproblem, SIAM J. Optim. 11 (2000) 611-646.
    • (2000) SIAM J. Optim. , vol.11 , pp. 611-646
    • Rojas, M.1    Santos, S.A.2    Sorensen, D.C.3
  • 16
    • 0001382978 scopus 로고
    • Newton's method with a model trust region modification
    • D.C. Sorensen, Newton's method with a model trust region modification, SIAM J. Numer. Anal. 19 (1982) 409-426.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 409-426
    • Sorensen, D.C.1
  • 17
    • 0000305846 scopus 로고
    • The conjugate gradient method and trust regions in large scale optimization
    • T. Steihaug, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal. 20 (1983) 626-637.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 626-637
    • Steihaug, T.1
  • 18
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • ed. I.S. Duff (Academic Press, London)
    • P.L. Toint, Towards an efficient sparsity exploiting Newton method for minimization, in: Sparse Matrices and Their Uses, ed. I.S. Duff (Academic Press, London, 1981) pp. 57-88.
    • (1981) Sparse Matrices and Their Uses , pp. 57-88
    • Toint, P.L.1
  • 19
    • 0347433923 scopus 로고    scopus 로고
    • On the truncated conjugate gradient method
    • Y. Yuan, On the truncated conjugate gradient method, Math. Programing Ser. A 87 (2000) 561-573.
    • (2000) Math. Programing Ser. A , vol.87 , pp. 561-573
    • Yuan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.