If your goal is to set thresholds which are then used to group your data into subgroups, the answer is no. Sorry. Why?
Think about it. Change the threshold just by a tiny amount. As long as it does not change what subgroups the data falls in, it changes nothing about your objective. So your function becomes a piecewise constant function of the parameters, thus discontinuous, non-differentiable, etc. No optimizer will handle this well, certainly not one that assumes differentiability.
So, it is not a problem to have multiple unknowns for that optimizer. What you cannot have is a discontinuous function. You also cannot solve for multiple VARIABLES. Group all of your unknowns into ONE vector of unknowns.
