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Nocedal, Jorge

Updating quasi-Newton matrices with limited storage. (English) Zbl 0464.65037

Math. Comput. 35, 773-782 (1980).
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Cited in 3 Reviews
Cited in 262 Documents

MSC:

65K05 Numerical mathematical programming methods
65F30 Other matrix algorithms (MSC2010)
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming

Keywords:

symmetric updates; Broyden-Fletcher-Goldfarb-Shanno quasi-Newton update; least-change formulas; numerical experiments; standard test functions; preconditioned conjugate gradient methods

Citations:

Zbl 0356.65041

Software:

DRVOCR
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\textit{J. Nocedal}, Math. Comput. 35, 773--782 (1980; Zbl 0464.65037)
Full Text: DOI

References:

[1] C. G. Broyden, The convergence of a class of double-rank minimization algorithms. II. The new algorithm, J. Inst. Math. Appl. 6 (1970), 222 – 231. · Zbl 0207.17401
[2] A. G. Buckley, A combined conjugate-gradient quasi-Newton minimization algorithm, Math. Programming 15 (1978), no. 2, 200 – 210. · Zbl 0386.90051
[3] W. C. DAVIDON & L. NAZARETH, DRVOCR-A FORTRAN Implementation of Davidon’s Optimally Conditioned Method, TM-306, Argonne National Lab., Argonne, Ill., 1977.
[4] J. E. Dennis Jr. and Jorge J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev. 19 (1977), no. 1, 46 – 89. · Zbl 0356.65041
[5] R. FLETCHER, ”A new approach to variable metric algorithms,” Comput. J., v. 13, 1970, pp. 317-322. · Zbl 0207.17402
[6] Hermann Matthies and Gilbert Strang, The solution of nonlinear finite element equations, Internat. J. Numer. Methods Engrg. 14 (1979), no. 11, 1613 – 1626. · Zbl 0419.65070
[7] L. NAZARETH, A Relationship Between the BFGS and Conjugate Gradient Algorithms, ANL-AMD Tech. Memo 282 (rev.), Argonne National Lab., Argonne, Ill., 1977.
[8] L. NAZARETH & J. NOCEDAL, A Study of Conjugate Gradient Methods, Tech. Rep. SOL 78-29, Dept. of Operations Research, Stanford University, Stanford, Calif., 1979. · Zbl 0482.90078
[9] L. NAZARETH & J. NOCEDAL, ”Convergence analysis of optimization methods that use variable storage,” Manuscript, 1978.
[10] A. PERRY, A Modified Conjugate Gradient Algorithm, Discussion paper No. 229, Center for Mathematical Studies in Economics and Management Science, Northwestern University, Evanston, Ill., 1976.
[11] D. SHANNO, Conjugate Gradient Methods With Inexact Line Searches, MIS Tech. Report 22, University of Arizona, Tucson, Ariz., 1977.
[12] D. SHANNO, On Variable-Metric Methods for Sparse Hessians, MIS Tech. Rep. 27, University of Arizona, Tucson, Ariz., 1978. · Zbl 0424.65027
[13] D. SHANNO & K. PHUA, A Variable Method Subroutine for Unconstrained Nonlinear Minimization, MIS Tech. Rep. No. 28, University of Arizona, Tucson, Ariz., 1978.
[14] Josef Stoer, On the convergence rate of imperfect minimization algorithms in Broyden’s \?-class, Math. Programming 9 (1975), no. 3, 313 – 335. · Zbl 0346.90047
[15] Ph. L. Toint, On sparse and symmetric matrix updating subject to a linear equation, Math. Comp. 31 (1977), no. no 140, 954 – 961. · Zbl 0379.65034
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