Reformulations in Mathematical Programming: Definitions

The mathematical programming formulation language is a very powerful tool used to formalize optimization problems by means of parameters, decision variables, objective functions and constraints. Such diverse settings as combinatorial, integer, continuous, linear and nonlinear optimization problems can be defined precisely by their corresponding mathematical programming formulations. Its power is not limited to its expressiveness, but usually allows hasslefree solution of the problem: most general-purpose solution algorithms solve optimization problems cast in their mathematical programming formulation, and the corresponding implementations can usually be hooked into language environments which allow the user to input and solve complex optimization problems easily. It is well known that several different formulations may share the same numerical properties (feasible region, optima) though some of them are easier to solve than others with respect to the most efficient available algorithms. Being able to cast the problem in the best possible formulation is therefore a crucial aspect of any solution process.