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Numerical Methods and Optimization in Finance by Enrico Schumann, Dietmar Maringer, Manfred Gilli

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Figure 11.12 Detailed starting simplex and two reflections.

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))f(x(2))f(x(n+1))image (right panel). We then compute the mean over all vertices except the worst (the one with the highest function value):

x¯=1ni=1nx(i)  i=1,,n.

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

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