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

Konstantin Avrachenkov, Vladimir Ejov, and Jerzy A. Filar. "On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs." Banach Center Publications 71.1 (2006): 29-38. <http://eudml.org/doc/282316>.

@article{KonstantinAvrachenkov2006,
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 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.},
author = {Konstantin Avrachenkov, Vladimir Ejov, Jerzy A. Filar},
journal = {Banach Center Publications},
keywords = {parametric mathematical programming},
language = {eng},
number = {1},
pages = {29-38},
title = {On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs},
url = {http://eudml.org/doc/282316},
volume = {71},
year = {2006},
}

TY - JOUR
AU - Konstantin Avrachenkov
AU - Vladimir Ejov
AU - Jerzy A. Filar
TI - On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs
JO - Banach Center Publications
PY - 2006
VL - 71
IS - 1
SP - 29
EP - 38
AB - 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.
LA - eng
KW - parametric mathematical programming
UR - http://eudml.org/doc/282316
ER -