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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-1,
author = {Ha Huy Vui and Pham Tien Son},
title = {On the \L ojasiewicz exponent at infinity of real polynomials},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {197-208},
zbl = {1153.14034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-1}
}
Ha Huy Vui; Pham Tien Son. On the Łojasiewicz exponent at infinity of real polynomials. Annales Polonici Mathematici, Tome 93 (2008) pp. 197-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-1/