I have a non-function (not in closed form) that takes in a few parameters (about 20) and returns a real value. A few of these parameters are discrete while others are continuous. Some of these parameters can only be chosen from a finite space of values.
Since I don't have the function in closed form, I cannot use any gradient based methods. However, the discrete nature and the boxed constraints on a few of those parameters restrict even the number of derivative free optimization techniques at my disposal. I am wondering what are the options in terms of optimization methods that I can use.