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 ε. 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 ε in a neighbourhood of ε = 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-2,
author = {Konstantin Avrachenkov and Vladimir Ejov and Jerzy A. Filar},
title = {On Newton's polygons, Gr\"obner bases and series expansions of perturbed polynomial programs},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {29-38},
zbl = {1119.13023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-2}
}
Konstantin Avrachenkov; Vladimir Ejov; Jerzy A. Filar. On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs. Banach Center Publications, Tome 72 (2006) pp. 29-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-2/