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Cited by 8,560

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

On the limited memory BFGS method for large scale optimization

Liu, Dong C., Nocedal, Jorge·1989·Mathematical Programming
DOI 10.1007/bf01589116
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Citations

Cites

  • Practical Optimization

    Gill, P. E., Murray, W., & Wright, M. H. (2019) · doi:10.1137/1.9781611975604 · Cited by 1,737 · cited 1×

    “…see for example Steihaug (1983), O'Leary (1982), Toint (1981) and Nash (1985); (ii) the partitioned quasi-Newton method of Griewank and Toint (1982a); (iii) the conjugate gradient method; see for example Fletcher (1980) and Gill, Murray and Wright (1981); (iv) limited memory quasi-Newton methods.”
    Method

Research works printed but not linked: 34

  1. E.M.L. Beale, “Algorithms for very large nonlinear optimization problems,” in: M.J.D. Powell, ed.,Nonlinear Optimization 1981 (Academic Press, London, 1981) pp. 281–292.
  2. A. Buckley, “A combined conjugate gradient quasi-Newton minimization algorithm,”Mathematical Programming 15 (1978) 200–210. · DOI
  3. A. Buckley, “Update to TOMS Algorithm 630,” Rapports Techniques No. 91, Institut National de Recherche en Informatique et en Automatique, Domaine Voluceau, Rocquencourt, B.P. 105 (Le Chesnay, 1987).
  4. A. Buckley and A. LeNir, “QN-like variable storage conjugate gradients,”Mathematical Programming 27 (1983) 155–175. · DOI
  5. A. Buckley and A. LeNir, “BBVSCG—A variable storage algorithm for function minimization,”ACM Transactions on Mathematical Software 11/2 (1985) 103–119. · DOI
  6. R.H. Byrd and J. Nocedal, “A tool for the analysis of quasi-Newton methods with application to unconstrained minimization,”SIAM Journal on Numerical Analysis 26 (1989) 727–739. · DOI
  7. J.E. Dennis Jr. and R.B. Schnabel, “A view of unconstrained optimization,” in: G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J. Todd, eds.,Handbooks in Operations Research and Management Science, Vol. 1, Optimization (North-Holland, Amsterdam, 1989) pp. 1–72.
  8. R. Fletcher,Practical Methods of Optimization, Vol. 1, Unconstrained Optimization (Wiley, New York, 1980).
  9. J.C. Gilbert and C. Lemaréchal, “Some numerical experiments with variable storage quasi-Newton algorithms,” IIASA Working Paper WP-88, A-2361 (Laxenburg, 1988).
  10. P.E. Gill and W. Murray, “Conjugate-gradient methods for large-scale nonlinear optimization,” Technical Report SOL 79-15, Department of Operations Research, Stanford University (Stanford, CA, 1979). · DOI
  11. A. Griewank, “The global convergence of partitioned BFGS on semi-smooth problems with convex decompositions,” ANL/MCS-TM-105, Mathematics and Computer Science Division, Argonne National Laboratory (Argonne, IL, 1987).
  12. A. Griewank and Ph.L. Toint, “Partitioned variable metric updates for large structured optimization problems,”Numerische Mathematik 39 (1982a) 119–137. · DOI
  13. A. Griewank and Ph.L. Toint, “Local convergence analysis of partitioned quasi-Newton updates,”Numerische Mathematik 39 (1982b) 429–448. · DOI
  14. A. Griewank and Ph.L. Toint, “Numerical experiments with partially separable optimization problems,” in: D.F. Griffiths, ed.,Numerical Analysis: Proceedings Dundee 1983, Lecture Notes in Mathematics, Vol. 1066 (Springer, Berlin, 1984) pp. 203–220. · DOI
  15. D.C. Liu and J. Nocedal, “Test results of two limited memory methods for large scale optimization,” Technical Report NAM 04, Department of Electrical Engineering and Computer Science, Northwestern University (Evanston, IL, 1988).
  16. J.J. Moré, B.S. Garbow and K.E. Hillstrom, “Testing unconstrained optimization software,”ACM Transactions on Mathematical Software 7 (1981) 17–41. · DOI
  17. S.G. Nash, “Preconditioning of truncated-Newton methods,”SIAM Journal on Scientific and Statistical Computing 6 (1985) 599–616. · DOI
  18. L. Nazareth, “A relationship between the BFGS and conjugate gradient algorithms and its implications for new algorithms,”SIAM Journal on Numerical Analysis 16 (1979) 794–800. · DOI
  19. J. Nocedal, “Updating quasi-Newton matrices with limited storage,”Mathematics of Computation 35 (1980) 773–782. · DOI
  20. D.P. O'Leary, “A discrete Newton algorithm for minimizing a function of many variables,”Mathematical Programming 23 (1982) 20–33. · DOI
  21. J.D. Pearson, “Variable metric methods of minimization,”Computer Journal 12 (1969) 171–178. · DOI
  22. J.M. Perry, “A class of conjugate gradient algorithms with a two-step variable-metric memory,” Discussion Paper 269, Center for Mathematical Studies in Economics and Management Science, Northwestern University (Evanston, IL, 1977).
  23. M.J.D. Powell, “Some global convergence properties of a variable metric algorithm for minimization without exact line search,” in: R.W. Cottle and C.E. Lemke, eds.,Nonlinear Programing, SIAM-AMS Proceedings IX (SIAM, Philadelphia, PA, 1976).
  24. M.J.D. Powell, “Restart procedures for the conjugate gradient method,”Mathematical Programming 12 (1977) 241–254. · DOI · Paper page
  25. D.F. Shanno, “On the convergence of a new conjugate gradient algorithm,”SIAM Journal on Numerical Analysis 15 (1978a) 1247–1257. · DOI
  26. D.F. Shanno, “Conjugate gradient methods with inexact searches,”Mathematics of Operations Research 3 (1978b) 244–256. · DOI · Paper page
  27. D.F. Shanno and K.H. Phua, “Matrix conditioning and nonlinear optimization,”Mathematical Programming 14 (1978) 149–160. · DOI
  28. D.F. Shanno and K.H. Phua, “Remark on algorithm 500: minimization of unconstrained multivariate functions,”ACM Transactions on Mathematical Software 6 (1980) 618–622. · DOI · Paper page
  29. T. Steihaug, “The conjugate gradient method and trust regions in large scale optimization,”SIAM Journal on Numerical Analysis 20 (1983) 626–637. · DOI
  30. Ph.L. Toint, “Some numerical results using a sparse matrix updating formula in unconstrained optimization,”Mathematics of Computation 32 (1978) 839–851. · DOI
  31. Ph.L. Toint, “Towards an efficient sparsity exploiting Newton method for minimization,” in: I.S. Duff, ed.,Sparse Matrices and their Uses (Academic Press, New York, 1981) pp. 57–87.
  32. Ph.L. Toint, “Test problems for partially separable optimization and results for the routine PSPMIN,” Report Nr 83/4, Department of Mathematics, Facultés Universitaires de Namur (Namur, 1983a).
  33. Ph.L. Toint, “VE08AD, a routine for partially separable optimization with bounded variables,” Harwell Subroutine Library, A.E.R.E. (UK, 1983b).
  34. Ph.L. Toint, “A view of nonlinear optimization in a large number of variables,” Report Nr 86/16, Department of Mathematics, Facultés Universitaires de Namur (Namur, 1986).

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Metadata

Authors
Liu, D. C., & Nocedal, J.
Venue
Mathematical Programming
Publisher
Springer Science and Business Media LLC
Published
1989-08
Volume
45
Issue
1-3
Pages
503-528
ISSN
  • 0025-5610 (ISSN-L)
  • 1436-4646
DOI
10.1007/bf01589116
OpenAlex
W2051434435
Cited by
8,560
References
1
FWCI
10.93
Type
journal article
Language
en
Open access
closed
Licence
www.springer.com/tdm (tdm)

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