Linear program with higher order non-linear constraints.
I am not sure whether I have posted the question on the right place or not as I was unable to find the optimization forum.
I want to solve a linear objective function, with some linear constraints and one higher order non-linear (not quadratic, it Lp-norm) constraint.
I know that Lp-norm constraint can be approximated by second order taylor series, and the problem is solved by mosek. But the approximating Lp-norm with taylor series seems not a good thing for my case.
Can any tell me how to solve an optimization problem with general non-linear constraints. Or can any one suggest a solver that can do it if I give my optimization problem to it.
Secondly can any one guide me when the use of second order taylor series for approximating a function is appropriate (for example whether it is appropriate for Lp-norm or not), and what will be approximation error.