Non-linear regression to find minimum

Hi all !

I need to find the minimum of a multiple variables non-linear discrete
function, and I'm not a mathematician...

More specifically: I have a few hundreds thousands of data points
(X1,X2,...,Xn,Y) where the Xn are the variables and Y is the result of
the function that I would like to minimize.

My guess is that the best approach would be to do a non-linear
regression and then find the minimum: would that be the right
approach?

If yes, is MatLab the right tool to do this?

Many thanks for your help!
Regards,
Thomas

PS: my function has 23 variables but, if this is a limitation, I could
reduce it (and have a more rough approach).

.