메뉴 건너뛰기




Volumn 9, Issue 2, 1999, Pages 504-525

Solving the trust-region subproblem using the Lanczos method

Author keywords

Conjugate gradients; Lanczos method; Preconditioning; Trust region subproblem

Indexed keywords


EID: 0033437435     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623497322735     Document Type: Article
Times cited : (259)

References (23)
  • 2
    • 0003141840 scopus 로고
    • LANCELOT: A fortran package for large-scale nonlinear optimization (release A)
    • Springer-Verlag, Heidelberg, Berlin, New York
    • A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A), Springer Series in Computational Mathematics 17, Springer-Verlag, Heidelberg, Berlin, New York, 1992.
    • (1992) Springer Series in Computational Mathematics , pp. 17
    • Conn, A.R.1    Gould, N.I.M.2    Toint, Ph.L.3
  • 3
    • 0018505838 scopus 로고
    • Two new unconstrained optimization algorithms which use function and gradient values
    • J E. DENNIS AND H. H. W. MEI, Two new unconstrained optimization algorithms which use function and gradient values, J. Optim. Theory Appl., 28 (1979), pp. 453-482.
    • (1979) J. Optim. Theory Appl. , vol.28 , pp. 453-482
    • Dennis, J.E.1    Mei, H.H.W.2
  • 4
    • 0000955796 scopus 로고
    • Computing optimal locally constrained steps
    • D. M. GAY, Computing optimal locally constrained steps, SIAM J. Sei. Statist. Comput., 2 (1981), pp. 186-197.
    • (1981) SIAM J. Sei. Statist. Comput. , vol.2 , pp. 186-197
    • Gay, D.M.1
  • 5
    • 0001237594 scopus 로고
    • Maximization by quadratic hill-climbing
    • S. M. GOLDFELDT, R. E. QUANDT, AND H. F. TROTTER, Maximization by quadratic hill-climbing, Econometrica, 34 (1966), pp. 541-551.
    • (1966) Econometrica , vol.34 , pp. 541-551
    • Goldfeldt, S.M.1    Quandt, R.E.2    Trotter, H.F.3
  • 6
    • 0040847421 scopus 로고    scopus 로고
    • A catalogue of subroutines (release 13)
    • Harwell, Oxfordshire, England, to appear
    • HARWELL SUBROUTINE LIBRARY, A Catalogue of Subroutines (Release 13), AEA Technology, Harwell, Oxfordshire, England, 1998, to appear.
    • (1998) AEA Technology
  • 8
    • 0030672155 scopus 로고    scopus 로고
    • Numerical experience with new truncated Newton methods in large scale unconstrained optimization
    • S. LUCIDI AND M. ROMA, Numerical experience with new truncated Newton methods in large scale unconstrained optimization, Comput. Optim. Appl., 7 (1997), pp. 71-87.
    • (1997) Comput. Optim. Appl. , vol.7 , pp. 71-87
    • Lucidi, S.1    Roma, M.2
  • 10
    • 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
  • 11
    • 0003668665 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ; reprinted by SIAM, Philadelphia, PA
    • B. N. PARLETT, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980; reprinted by SIAM, Philadelphia, PA, 1998.
    • (1980) The Symmetric Eigenvalue Problem
    • Parlett, B.N.1
  • 12
    • 0012756718 scopus 로고
    • Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems
    • B. N. PARLETT AND J. K. REID, Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems, J. Inst. Math. Appl., 1 (1981), pp. 135-155.
    • (1981) J. Inst. Math. Appl. , vol.1 , pp. 135-155
    • Parlett, B.N.1    Reid, J.K.2
  • 13
    • 0002340344 scopus 로고
    • A new algorithm for unconstrained optimization
    • J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds., Academic Press, London, New York
    • M. J. D. POWELL, A new algorithm for unconstrained optimization, in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds., Academic Press, London, New York, 1970, pp. 31-65.
    • (1970) Nonlinear Programming , pp. 31-65
    • Powell, M.J.D.1
  • 14
    • 0002302301 scopus 로고
    • Convergence properties of a class of minimization algorithms
    • O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, London, New York
    • M. J. D. POWELL, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press, London, New York, 1975, pp. 1-27.
    • (1975) Nonlinear Programming , vol.2 , pp. 1-27
    • Powell, M.J.D.1
  • 15
    • 0029425729 scopus 로고
    • Max-min eigenvalue problems, primal-dual interior point algorithms, and trust region subproblems
    • F. RENDL, R. J. VANDERBEI, AND H. WOLKOWICZ, Max-min eigenvalue problems, primal-dual interior point algorithms, and trust region subproblems, Optim. Methods Softw., 5 (1995), pp. 1-16.
    • (1995) Optim. Methods Softw. , vol.5 , pp. 1-16
    • Rendl, F.1    Vanderbei, R.J.2    Wolkowicz, H.3
  • 16
    • 0031141179 scopus 로고    scopus 로고
    • A semidefinite framework for trust region subproblems with applications to large scale minimization
    • F. RENDL AND H. WOLKOWICZ, A semidefinite framework for trust region subproblems with applications to large scale minimization, Math. Programming, Series B, 77 (1997), pp. 273-299.
    • (1997) Math. Programming, Series B , vol.77 , pp. 273-299
    • Rendl, F.1    Wolkowicz, H.2
  • 19
    • 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
  • 20
    • 0001382978 scopus 로고
    • Newton's method with a model trust modification
    • D. C. SORENSEN, Newton's method with a model trust modification, SIAM J. Numer. Anal., 19 (1982), pp. 409-426.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 409-426
    • Sorensen, D.C.1
  • 21
    • 0031542396 scopus 로고    scopus 로고
    • Minimization of a large-scale quadratic function subject to a spherical constraint
    • D. C. SORENSEN, Minimization of a large-scale quadratic function subject to a spherical constraint, SIAM J. Optim., 7 (1997), pp. 141-161.
    • (1997) SIAM J. Optim. , vol.7 , pp. 141-161
    • Sorensen, D.C.1
  • 22
    • 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), pp. 626-637.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 626-637
    • Steihaug, T.1
  • 23
    • 0002633896 scopus 로고
    • Towards an efficient sparsity exploiting Newton method for minimization
    • S. Duff, ed., Academic Press, London, New York
    • PH. L. TOINT, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, New York, 1981, pp. 57-88.
    • (1981) Sparse Matrices and Their Uses , vol.1 , pp. 57-88
    • Toint, Ph.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.