On Newton's polygons Grobner bases and series expansions of perturbed polynomial programs

In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter e. Recently, the theory of Grobner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in e in a neighbourhood of e = 0. In this paper we show that the determination of the branching order and the order of the pole (if any) of these Puiseux series can be achieved by invoking a classical technique known as the "Newton's polygon" and using it in conjunction with the Grobner bases techniques.