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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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  • $\begingroup$ You'd better post the relevant paper here, so we could take a look at it. $\endgroup$
    – Sunni
    Apr 27, 2010 at 13:24
  • $\begingroup$ I don't have the access to the paper :( If I had, I probably wouldn't need to ask the question. $\endgroup$
    – Katastrofa
    Apr 27, 2010 at 14:01
  • $\begingroup$ This strategy is also described here: math.lsu.edu/~hozhang/papers/cgsurvey.pdf $\endgroup$
    – Katastrofa
    Apr 27, 2010 at 17:17
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    $\begingroup$ 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. $\endgroup$ Aug 12, 2010 at 22:56

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