On the Łojasiewicz exponent at infinity of real polynomials

• Autorzy: Ha Huy Vui , Pham Tien Son
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 3
• Strony: 197-208

Daty

wydano

2008

Twórcy

autor

Ha Huy Vui

• Institute of Mathematics, 18, Hoang Quoc Viet Road, Cau Giay District 10307, Hanoi, Vietnam

autor

Pham Tien Son

• Department of Mathematics, University of Dalat, Dalat, Vietnam

Identyfikatory

DOI

10.4064/ap94-3-1