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arXiv · 1411.7696

Nonnegative Morse polynomial functions and polynomial optimization

Công-Trình Lê
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Abstract

In this paper we study the representation of Morse polynomial functions which are nonnegative on a compact basic closed semi-algebraic set in $\mathbb R^n$, 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.

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Công-Trình Lê. 2015-09-24. Nonnegative Morse polynomial functions and polynomial optimization. https://doi.org/10.1007/s11117-015-0367-z

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