Geodesic
On the /Lojasiewicz exponent at infinity of real polynomials
Ha Huy Vui1 ; Pham Tien Son2
1 Institute of Mathematics 18, Hoang Quoc Viet Road Cau Giay District 10307 Hanoi, Vietnam
2 Department of Mathematics University of Dalat Dalat, Vietnam
Annales Polonici Mathematici, Tome 94 (2008) no. 3, pp. 197-208.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $f \colon {\Bbb R}^n \rightarrow {\Bbb R}$ 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 /Lojasiewicz 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 /Lojasiewicz exponent at infinity of $f$ and the problem of computing the global optimum of $f$ is also established.
DOI : 10.4064/ap94-3-1
Mots-clés : colon bbb rightarrow bbb nonconstant polynomial function using information curve tangency provide method determine ojasiewicz exponent infinity corollary computational criterion decide lojasiewicz exponent infinity finite obtain formula calculate set points which polynomial proper moreover relation between lojasiewicz exponent infinity problem computing global optimum established

Ha Huy Vui 1 ; Pham Tien Son 2

1 Institute of Mathematics 18, Hoang Quoc Viet Road Cau Giay District 10307 Hanoi, Vietnam
2 Department of Mathematics University of Dalat Dalat, Vietnam 
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Ha Huy Vui; Pham Tien Son. On the /Lojasiewicz exponent at infinity of real polynomials. Annales Polonici Mathematici, Tome 94 (2008) no. 3, pp. 197-208. doi : 10.4064/ap94-3-1. http://geodesic.mathdoc.fr/articles/10.4064/ap94-3-1/

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