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Volumn 8, Issue 4, 1998, Pages 1060-1083

BFGS with update skipping and varying memory

Author keywords

BFGS; Broyden family; Limited memory; Minimization; Quasi Newton; Update skipping

Indexed keywords


EID: 0032333546     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623496306450     Document Type: Article
Times cited : (35)

References (30)
  • 4
    • 0039545486 scopus 로고
    • Tech. Report TR 1989CS-3, Mathematics, Statistics and Computing Centre, Dalhousie University, Halifax (CDN)
    • A. BUCKLEY, Test functions for unconstrained minimization, Tech. Report TR 1989CS-3, Mathematics, Statistics and Computing Centre, Dalhousie University, Halifax (CDN), 1989.
    • (1989) Test Functions for Unconstrained Minimization
    • Buckley, A.1
  • 5
    • 0028319529 scopus 로고
    • Representations of quasi-Newton matrices and their use in limited memory methods
    • R. H. BYRD, J. NOCEDAL, AND R. B. SCHNABEL, Representations of quasi-Newton matrices and their use in limited memory methods, Math. Programming, 63 (1994), pp. 129-156.
    • (1994) Math. Programming , vol.63 , pp. 129-156
    • Byrd, R.H.1    Nocedal, J.2    Schnabel, R.B.3
  • 7
    • 0020763823 scopus 로고
    • Truncated-Newton algorithms for large-scale unconstrained optimization
    • R. S. DEMBO AND T. STEIHAUG, Truncated-Newton algorithms for large-scale unconstrained optimization, Math. Programming, 26 (1983), pp. 190-212.
    • (1983) Math. Programming , vol.26 , pp. 190-212
    • Dembo, R.S.1    Steihaug, T.2
  • 8
    • 0004041275 scopus 로고
    • Numerical methods for unconstrained optimization and nonlinear equations
    • Prentice-Hall, Englewood Cliffs, NJ, Reprinted by Society for Industrial and Applied Mathematics, Philadelphia, PA
    • J. DENNIS AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Series in Computational Mathematics, Prentice-Hall, Englewood Cliffs, NJ, 1983. Reprinted by Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996.
    • (1983) Series in Computational Mathematics
    • Dennis, J.1    Schnabel, R.B.2
  • 9
    • 0040730832 scopus 로고
    • An optimal positive definite update for sparse Hessian matrices
    • Technical report, University of Dundee, Cited in [1, 2]
    • R. FLETCHER, An optimal positive definite update for sparse Hessian matrices, Numerical Analysis NA/145, Technical report, University of Dundee, 1992. Cited in [1, 2].
    • (1992) Numerical Analysis NA/145
    • Fletcher, R.1
  • 10
    • 85033893083 scopus 로고    scopus 로고
    • L-BFGS with Variations home page
    • T. GIBSON, D. O'LEARY, AND L. NAZARETH, L-BFGS with Variations home page, http://www.cs.umd.edu/users/oleary/LBFGS/index.html (1996).
    • (1996)
    • Gibson, T.1    O'Leary, D.2    Nazareth, L.3
  • 11
    • 0039755891 scopus 로고
    • Conjugate-gradient methods for large-scale nonlinear optimization
    • Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA
    • P. E. GILL AND W. MURRAY, Conjugate-gradient methods for large-scale nonlinear optimization, Tech. Report SOL 79-15, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, CA, 1979.
    • (1979) Tech. Report SOL 79-15
    • Gill, P.E.1    Murray, W.2
  • 13
    • 85033875351 scopus 로고
    • Private communication to authors of [3]. Cited in [1, 2]
    • N. GOULD, Private communication to authors of [3], 1989. Cited in [1, 2].
    • (1989)
    • Gould, N.1
  • 14
    • 0013358480 scopus 로고
    • Partitioned variable metric updates for large structured optimization problems
    • A. GRIEWANK AND P. L. TOINT, Partitioned variable metric updates for large structured optimization problems, Numer. Math., 39 (1982), pp. 119-137.
    • (1982) Numer. Math. , vol.39 , pp. 119-137
    • Griewank, A.1    Toint, P.L.2
  • 16
    • 33646887390 scopus 로고
    • On the limited memory BFGS method for large scale optimization
    • D. C. LIU AND J. NOCEDAL, On the limited memory BFGS method for large scale optimization, Math. Programming, 45 (1989), pp. 503-528.
    • (1989) Math. Programming , vol.45 , pp. 503-528
    • Liu, D.C.1    Nocedal, J.2
  • 19
    • 0021481124 scopus 로고
    • Newton-type minimization via the Lanczos process
    • S. NASH, Newton-type minimization via the Lanczos process, SIAM J. Numer. Anal., 21 (1984), pp. 770-788.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 770-788
    • Nash, S.1
  • 20
    • 0001684438 scopus 로고
    • A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization
    • S. G. NASH AND J. NOCEDAL, A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization, SIAM J. Optim., 1 (1991), pp. 358-372.
    • (1991) SIAM J. Optim. , vol.1 , pp. 358-372
    • Nash, S.G.1    Nocedal, J.2
  • 21
    • 0000554172 scopus 로고
    • A relationship between BFGS and conjugate gradient algorithms and its implications for new algorithms
    • L. NAZARETH, A relationship between BFGS and conjugate gradient algorithms and its implications for new algorithms, SIAM J. Numer. Anal., 16 (1979), pp. 794-800.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 794-800
    • Nazareth, L.1
  • 22
    • 85033876568 scopus 로고
    • unpublished manuscript, University of California at Berkeley, Berkeley, CA
    • L. NAZARETH, On the BFGS Method, unpublished manuscript, University of California at Berkeley, Berkeley, CA, 1981.
    • (1981) On the BFGS Method
    • Nazareth, L.1
  • 23
    • 84966262179 scopus 로고
    • Updating quasi-Newton matrices with limited storage
    • J. NOCEDAL, Updating quasi-Newton matrices with limited storage, Math. Comp., 35 (1980), pp. 773-782.
    • (1980) Math. Comp. , vol.35 , pp. 773-782
    • Nocedal, J.1
  • 24
    • 84972047841 scopus 로고
    • Theory of algorithms for unconstrained optimization
    • Cambridge University Press, London
    • J. NOCEDAL, Theory of algorithms for unconstrained optimization, in Acta Numerica (1991), Cambridge University Press, London, 1992, pp. 199-242.
    • (1991) Acta Numerica , pp. 199-242
    • Nocedal, J.1
  • 25
    • 0020129823 scopus 로고
    • A discrete Newton algorithm for minimizing a function of many variables
    • D. P. O'LEARY, A discrete Newton algorithm for minimizing a function of many variables, Math. Programming, 23 (1982), pp. 20-33.
    • (1982) Math. Programming , vol.23 , pp. 20-33
    • O'Leary, D.P.1
  • 26
    • 0039478111 scopus 로고
    • Self-scaling variable metric algorithms, Part II: Implementation and experiments
    • Cited in [1, 2]
    • S. OREN, Self-scaling variable metric algorithms, Part II: Implementation and experiments, Management Science, 20 (1974), pp. 863-874. Cited in [1, 2].
    • (1974) Management Science , vol.20 , pp. 863-874
    • Oren, S.1
  • 27
    • 0038952789 scopus 로고
    • Quadratic termination properties of minimization algorithms I: Statement and discussion of results
    • M. J. D. POWELL, Quadratic termination properties of minimization algorithms I: Statement and discussion of results, J. Inst. Math. Appl., 10 (1972), pp. 333-342.
    • (1972) J. Inst. Math. Appl. , vol.10 , pp. 333-342
    • Powell, M.J.D.1
  • 28
    • 0000618748 scopus 로고
    • Conjugate gradient methods with inexact line searches
    • D. F. SHANNO, Conjugate gradient methods with inexact line searches, Math. Oper. Res., 3 (1978), pp. 244-256.
    • (1978) Math. Oper. Res. , vol.3 , pp. 244-256
    • Shanno, D.F.1
  • 29
    • 84966243875 scopus 로고
    • Some numerical results using a sparse matrix updating formula in unconstrained optimization
    • P. TOINT, Some numerical results using a sparse matrix updating formula in unconstrained optimization, Math. Comput., 32 (1978), pp. 839-852.
    • (1978) Math. Comput. , vol.32 , pp. 839-852
    • Toint, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.