On the Łojasiewicz exponent at infinity of real polynomials

Ha Huy Vui, and Pham Tien Son. "On the Łojasiewicz exponent at infinity of real polynomials." Annales Polonici Mathematici 94.3 (2008): 197-208. <http://eudml.org/doc/280377>.

@article{HaHuyVui2008,
abstract = {Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing the global optimum of f is also established.},
author = {Ha Huy Vui, Pham Tien Son},
journal = {Annales Polonici Mathematici},
keywords = {Lojasiewicz exponent at infinity; real polynomial; proper map; global optimization problem},
language = {eng},
number = {3},
pages = {197-208},
title = {On the Łojasiewicz exponent at infinity of real polynomials},
url = {http://eudml.org/doc/280377},
volume = {94},
year = {2008},
}

TY - JOUR
AU - Ha Huy Vui
AU - Pham Tien Son
TI - On the Łojasiewicz exponent at infinity of real polynomials
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 3
SP - 197
EP - 208
AB - Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing the global optimum of f is also established.
LA - eng
KW - Lojasiewicz exponent at infinity; real polynomial; proper map; global optimization problem
UR - http://eudml.org/doc/280377
ER -