Mathematical Programming and Turing-completeness

Mathematical Programming (MP) is a formal language that formally describes solutions of optimization problems whose objective function and constraints are explicit algebraic/transcendental functions of a set of given parameters (the problem input) and decision variables (encoding the solution to the problem). The solution process is carried out by a solver. As for any programming language, one may ask whether MP is Turing-complete, i.e. whether it can simulate a Universal Turing Machine. We exhibit a simulation mechanism that lends itself practical uses, and illustrate some interesting applications to algorithmic analysis.