I am minimizing a scalar function of 5 variables which looks something like:(adsbygoogle = window.adsbygoogle || []).push({});

f(x1,...x5) = -x1*x2, if g(x1,...x5)=1

infinity, if g(x1,...x5)=0

where g is can only take on two values, and cannot be expressed in closed-form.

Because of the essential discontinuities in the domain, I figured I better try a derivative-free method like Nelder-Mead Simplex. I tried using the MATLAB fminsearch() implementation, and it is not performing too well. While it does converge (even for very low tolerances) it is not reaching the local minima. The function changes very little, if at all, between iterations. See the end of the post for a history of a typical optimization (first 30 iterations)

Does anybody have any idea how to tune the simplex method for this problem, or suggest an alternative optimizer?

Many thanks,

s.

Iteration Func-count min f(x) Procedure

0 1 -0.00157673

1 6 -0.00165556 initial simplex

2 7 -0.00165556 reflect

3 9 -0.00171195 expand

4 11 -0.00172117 reflect

5 13 -0.00188736 expand

6 14 -0.00188736 reflect

7 15 -0.00188736 reflect

8 17 -0.00194533 reflect

9 19 -0.00194533 contract inside

10 21 -0.00214186 expand

11 22 -0.00214186 reflect

12 24 -0.00215877 reflect

13 26 -0.00242805 expand

14 28 -0.00272589 expand

15 30 -0.00272589 contract inside

16 31 -0.00272589 reflect

17 33 -0.00272589 contract inside

18 35 -0.00272589 contract inside

19 37 -0.00274379 reflect

20 39 -0.00274379 contract inside

21 41 -0.00274379 contract inside

22 43 -0.00274379 contract inside

23 45 -0.00274379 contract inside

24 47 -0.00274379 contract inside

25 49 -0.00274379 contract inside

26 51 -0.00274379 contract inside

27 53 -0.00274379 contract inside

28 55 -0.00274379 contract inside

29 56 -0.00274379 reflect

30 58 -0.00278432 reflect

31 60 -0.00286262 reflect

32 62 -0.00286262 contract inside

33 63 -0.00286262 reflect

34 65 -0.00292913 expand

35 67 -0.00292913 contract inside

36 69 -0.00305228 expand

37 70 -0.00305228 reflect

38 72 -0.00327878 expand

39 73 -0.00327878 reflect

40 75 -0.00356812 expand

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# Minimizing 5-d discontinuous objective function - alternatives to N-M Simplex

Can you offer guidance or do you also need help?

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