# Nonlinear conjugate gradient update strategy by Dai and Yuan

In Nocedal and Wright book "Numerical Optimization", they describe on page 123 (formula 5.49) an update strategy for the beta parameter in the nonlinear conjugate gradient optimization, which was proposed by Dai and Yuan (SIAM Journal on Optimization, 10 (1999), pp. 177-182). Nocedal and Wright say that this strategy when used from 2nd iteration onwards guarantees global convergence. However, they don't mention what should be done during the first iterations. Is my guess, that it doesn't really matter which strategy used initially, correct?

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You'd better post the relevant paper here, so we could take a look at it. – Sunni Apr 27 '10 at 13:24
I don't have the access to the paper :( If I had, I probably wouldn't need to ask the question. – Katastrofa Apr 27 '10 at 14:01
This strategy is also described here: math.lsu.edu/~hozhang/papers/cgsurvey.pdf – Katastrofa Apr 27 '10 at 17:17
They might not, but it would seem safe to just start with Polak-Ribiere for the first few iterations (it having slightly better properties than Fletcher-Reeves), and then use that Dai-Yuan update in subsequent iterations. – J. M. Aug 12 '10 at 22:56
Many thanks. – Katastrofa Aug 17 '10 at 16:55