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Global convergence result for conjugate gradient methods

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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.

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Communicated by L. C. W. Dixon

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Hu, Y.F., Storey, C. Global convergence result for conjugate gradient methods. J Optim Theory Appl 71, 399–405 (1991).

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