Nonnegative Morse polynomial functions and polynomial optimization

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. Bivi\`{a}-Ausina, we introduce two classes of non-degenerate polynomials for wh...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-09
Main Author: Lê, Công-Trình
Format: Article
Language:English
Subjects:
Algebra
Functions (mathematics)
Mathematical analysis
Optimization
Polynomials
Representations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. Bivi\`{a}-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.
ISSN:2331-8422
DOI:10.48550/arxiv.1411.7696