Abstract
We wish to examine the conjugate gradient and quasi-Newton minimization algorithms. A relation noted by Nazareth is extended to an algorithm in which conjugate gradient and quasi-Newton search directions occur together and which can be interpreted as a conjugate gradient algorithm with a changing metric.
This is a preview of subscription content, log in via an institution to check access.
References
J.C. Allwright, “Improving the conditioning of optimal control problems using simple models”, in: D.J. Bell, ed.,Recent mathematical developments in control (Academic Press, London, 1972).
A.G. Buckley, “A combined conjugate-gradient quasi-Newton minimization algorithm”,Mathematical Programming, to appear.
R. Fletcher, “A new approach to variable metric algorithms”,Computer Journal 13 (1970) 317–322.
R. Fletcher, “Conjugate direction methods”, in: W. Murray, ed.,Numerical methods for unconstrained optimization, (Academic Press, London, 1972) pp. 73–86.
M.R. Hestenes and E.L. Stiefel, “Methods of conjugate gradients for solving linear systems”,Journal of Research of the National Bureau of Standards 49 (1952) 409–436.
G.E. Myers, “Properties of the conjugate gradient and Davidon methods”,Journal of Optimization Theory and Applications 2 (1968) 209–219.
L. Nazareth, “A relationship between the BFGS and conjugate gradient algorithms”, AMD Tech. Memo 282, Argonne National Laboratory (1977).
M.J.D. Powell, “Restart procedures for the conjugate gradient method”,Mathematical Programming 12 (1977) 241–254.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Buckley, A. Extending the relationship between the conjugate gradient and BFGS algorithms. Mathematical Programming 15, 343–348 (1978). https://doi.org/10.1007/BF01609038
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01609038