I am trying to numerically solve a maximization problem where the control variables are implicitly defined in six nonlinear constraints. So basically something like this:
where G(x,k)=0, F>0, x>0
Where x is a vector of two variables, k is a vector of 6 other variables and G(x,k) are six non-linear constraints involving all the variables.
I'd really appreciate it if someone can tell me how to go about numerically solving this problem.