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arXiv · 1708.04075

On types of degenerate critical points of real polynomial functions

Feng Guo·Tien-Son Pham
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Abstract

In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point $c$, which is degenerate, of a multivariate polynomial function $f$. To this end, we introduce the definition of faithful radius of $c$ by means of the curve of tangency of $f$. We show that the type of $c$ can be determined by the global extrema of $f$ over the Euclidean ball centered at $c$ with a faithful radius.We propose algorithms to compute a faithful radius of $c$ and determine its type.

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Feng Guo, Tien-Son Pham. 2017-08-14. On types of degenerate critical points of real polynomial functions. https://arxiv.org/abs/1708.04075

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