We now detail the rules according to which the simplex evolves toward the minimum. Consider a function depending on *n* variables. Then, at iteration *k*, the simplex is defined by the vertices *x*^{(i)}, *i* = 1,…,*n* + 1 (left panel in following figure). These vertices are renamed such that $f({x}^{(1)})\le f({x}^{(2)})\le \cdots \le f({x}^{(n+1)})$ (right panel). We then compute the mean over all vertices except the worst (the one with the highest function value):

$\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{x}^{(i)}}\text{}i=1,\dots ,n.$

The vertex *x*_{n+1} with the worst function ...

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