×

zbMATH — the first resource for mathematics

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

MSC:
65K05 Numerical mathematical programming methods
65F30 Other matrix algorithms (MSC2010)
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming
Software:
DRVOCR
PDF BibTeX XML Cite
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 · doi:10.1007/BF01609018 · doi.org
[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. MorĂ©, Quasi-Newton methods, motivation and theory, SIAM Rev. 19 (1977), no. 1, 46 – 89. · Zbl 0356.65041 · doi:10.1137/1019005 · doi.org
[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 · doi:10.1002/nme.1620141104 · doi.org
[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 · doi:10.1007/BF01681353 · doi.org
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.