Optimization Algorithm - Nelder-Mead Simplex

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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.

 

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