How does fminsearch generate initial simplex ?

Question

Pragya Srivastava 2017-5-10

1
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https://ww2.mathworks.cn/matlabcentral/answers/339661-how-does-fminsearch-generate-initial-simplex

回答： Alan Weiss 2017-5-10

Hi, I want to understand how fminsearch generates its initial simplex with n+1 vertices, given the initial choice of parameters specified by user. For example : if I have to minimise and function f(p) where p=[p1,p2], and I supply an initial p0=[p1in p2in], then fminsearch should first generate a set of 3, 2-d points for simplex method. two of these points can be [p1in 0] and [0 p2in], but how is the third point constructed ?

Also, as a reverse problem, how are the final vertices of (n+1)-dim simplex converted to the values of optimum [p1_opt,p2_opt]. Does fminsearch takes some projection of final vertices along the parameter axes ?