, Volume 71, Issue 2, pp 399-405

Global convergence result for conjugate gradient methods

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Conjugate gradient optimization algorithms depend on the search directions, $$\begin{gathered} s^{(1)} = - g^{(1)} , \hfill \\ s^{(k + 1)} = - g^{(k + 1)} + \beta ^{(k)} s^{(k)} ,k \geqslant 1, \hfill \\ \end{gathered} $$ with different methods arising from different choices for the scalar β(k). In this note, conditions are given on β(k) to ensure global convergence of the resulting algorithms.

Communicated by L. C. W. Dixon