Mathematical programming is Turing-complete

We define mathematical programming (MP) as a formal language. We then show a MP formulation (of the MINLP class) whose parameters encode the input of a Minsky’s Register Machine (MRM) and whose set of solutions is the output of the MRM. Since the MRM is Turing-equivalent to a Universal Turing Machine (UTM), MP is Turing-complete. We show a few interesting applications deriving from treating MP as a formal language.