Choose parameters which minimize a function

I have two arrays 13x2 with points x,y for the first array and x',y' for the second array. I also have a function of x and x' and i want to chose 8 x and 8 x' from the arrays, such that minimize this function. This function takes arrays of 8 with x and x'. Have you got any idea?

Answer 1

[dpb]

Not sure I follow the intend exactly, but if I understand you wish to pick the subset of (8) values from each of two larger sets of (13) that minimizes a function of the two. Since

>> nchoosek(13,8)
ans =
      1287

and there are two combinations of these, brute-force enumeration will be time-consuming.

The thought that comes to mind would be to use one of the minimization routines and solve in a least squares sense (linear or nonlinear, depending on the functional form is the reason for the genericity rather than a specific routine) and the choose the coefficients that are nearest in magnitude to those. That doesn't guarantee that is the minimum but would likely be a reasonable guesstimate unless the model is extremelty sensitive to one (or more) coefficient.