how to write CustomStartPointSet if local minimum points are known?

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Nourhan Elsayed 2020-10-7

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i am using solver of fmincon ,and i want to create ptmatrix of starting points to use multistart algorithm.

so i can apply the command

tpoints = CustomStartPointSet(ptmatrix)

if the exact local minimum points are known, say S1, S2, S3, whereas S1 = [x1, x2, x3, ....] and S2 = [x1, x2, x3, ...] and so on. my approach is taking a point that is close to S1 and define it as pt.1 which is [x1, x2, x3, ...] and define pt.2 pt.3 as well.

the question is, what is the mathematical relationship between S and pt. how i can defin that .

any reference for documentation is highly appreciated

Thanks in advance