I'm facing the following problem. I have an unknown function with a very few known parameter-output sets according to the following:
|param1 |param2 |output |
--+--------+--------+--------+
1 | 0 | 0 | 43 |
2 | 0 | 100 | 36 |
3 | 500 | 100 | 66 |
4 | 1000 | 0 | 88 |
5 | 100 | 1000 | 61 |
6 | 500 | 500 | 78 |
I want to find the parameters at the optimum (maximum) of the function (with the additional condition that the sum of param1+param2 cannot be larger than 1000). How could that optimum calculated?
My idea is to find an approximation/candidate function based on the few data above, and then find it's optimum (with Nelder-Mead search or similar method). Is it a correct way? If so, what is the way to find the approximation function (by some regression, I guess, but this being an unsupervised task, how to set the power of the polynomial that describe the hyperplane in order not to be too high order)?
Thanks for any hints.