Some convergence properties of the conjugate gradient method View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1976-12

AUTHORS

M. J. D. Powell

ABSTRACT

It has been conjectured that the conjugate gradient method for minimizing functions of several variables has a superlinear rate of convergence, but Crowder and Wolfe show by example that the conjecture is false. Now the stronger result is given that, if the objective function is a convex quadratic and if the initial search direction is an arbitrary downhill direction, then either termination occurs or the rate of convergence is only linear, the second possibility being more usual. Relations between the starting point and the initial search direction that are necessary and sufficient for termination in the quadratic case are studied. More... »

PAGES

42-49

Journal

TITLE

Mathematical Programming

ISSUE

1

VOLUME

11

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01580369

DOI

http://dx.doi.org/10.1007/bf01580369

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005266469


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