Nonnegative Morse polynomial functions and polynomial optimization
arXiv:1411.7696 · doi:10.1007/s11117-015-0367-z
Abstract
In this paper we study the representation of Morse polynomial functions which are nonnegative on a compact basic closed semi-algebraic set in , and having only finitely many zeros in this set. Following C. Bivià-Ausina, we introduce two classes of non-degenerate polynomials for which the algebraic sets defined by them are compact. As a consequence, we study the representation of nonnegative Morse polynomials on these kinds of non-degenerate algebraic sets. Moreover, we apply these results to study the polynomial optimization problem for Morse polynomial functions.
Title changed, one reference added and one reference deleted. To appear in Positivity. Dedicated to Professor Hà Huy Vui on the occasion of his 65th birthday. in Positivity (2016)