Choosing the initial simplex in the Nelder-Mead optimization algorithm

Question

What\'s the best way to initialize a simplex for use in a Nelder-Mead simplex search from a user\'s \'guess\' vertex?

Answer 1

I think there is no general rule to determine best the initial simplex of the Nelder-Mead optimization because this required at least a vague knowledge of the response surface.

However, it can be a reasonable policy to set the points in such a way that the simplex covers virtually the entire possible range. The algorithm of Nelder-Mead will shrink automatically the simplex and aproximate to the optimum. The practical advantage of this policy is that you will obtain a better overall-knowledge of the response-function.

We have done some tests with HillStormer("http://www.berkutec.com"). This program permits to test these policies on testfunctons and we found that this plicy works rather well.

Please remember that the first simplex-opereation is añways a reflection. If the starting simplex covers the whole permitted range the reflection necessarily will give a point off limits. But HillStormer allows to use linear constraints and can avoid this problem.

You can find some more information in the system-help of HillStormer.

B. Kühne