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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 $f\left({x}^{\left(1\right)}\right)\le f\left({x}^{\left(2\right)}\right)\le \cdots \le f\left({x}^{\left(n+1\right)}\right)$ (right panel). We then compute the mean over all vertices except the worst (the one with the highest function value):

The vertex xn+1 with the worst function ...

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