In FAQ, you mentioned that NumXL is using Nelder-Mead Simplex optimization and you apply the constraints as a penalty terms into the utility function.

I guess you penalize since this is easier than maximize subject to constraints, but why not re-parametrize? For instance, for GARCH parameters you may use exponential or logistic, for ARMA you can maximize over the polynomial roots which by an exponential transformation could be easily constrained.