Let's say I have a function $f$ that I want to maximize. This function depends on many parameters $p_1, p_2, \dots, p_n$ (where $n > 20$). However, one parameter is a function of all the other parameters, e.g., $p_1 = p_1(p_2,\dots, p_n)$.
What are numerical algorithms to determine the maximum of $f$? I can provide certain boundaries on the parameters.