On the equivalence of the method of conjugate gradients and quasi-Newton methods on quadratic problems
(English)In: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894Article in journal (Other academic) Submitted
In this paper we state necessary and sufficient conditions for equivalence of the method of conjugate gradients and quasi-Newton methods on a quadratic problem. We show that the set of quasi-Newton schemes that generate parallel search directions to those of the method of conjugate gradients is strictly larger than the one-parameter Broyden family. In addition, we show that this set contains an infinite number of symmetric rank-one update schemes.
method of conjugate gradients, quasi-Newton method, uncon- strained quadratic program
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-166674OAI: oai:DiVA.org:kth-166674DiVA: diva2:811790
FunderSwedish Research Council
QS 20152015-05-132015-05-132015-05-19Bibliographically approved