On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs
Volume 71 / 2006
Banach Center Publications 71 (2006), 29-38
MSC: 34D15, 13P10, 65K10.
DOI: 10.4064/bc71-0-2
Abstract
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 $\varepsilon.$ Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in $\varepsilon$ in a neighbourhood of $\varepsilon =0$. 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 Gröbner bases techniques.
