4
$\begingroup$

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.

enter image description here

$\endgroup$
  • $\begingroup$ You always replace the worst point. Makes sense to me. $\endgroup$ – David Ketcheson Jul 1 '12 at 9:46
4
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.