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I am reading the following file, that explain the Nelder-Mead optimization Algorithm.(Algorithm Below) Where $B$ is the best point, $G$ second best point, $W$ is the worst point, $R$ reflection point. Why in Case(i) $W$ is replaced by $R$ ?

Assuming that $f(R)<f(G)$ than we go in $Case(i)$. If $f(B) < f(R)$ is true, than $f(B)<f(R)<f(G)$, in other words $R$ is better choice than $G$, but worst than $B$. According to the algorithm, $R$ should replace $W$, which doesn't make sense. Either the paper has an error, or I don't understand something.

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  • $\begingroup$ You always replace the worst point. Makes sense to me. $\endgroup$ – David Ketcheson Jul 1 '12 at 9:46
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R isn't the "reflection point" but the "reflected point", i.e., it lies on the other side of the simplex as viewed from the worst point. It should then all make sense.

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