Commun. Korean Math. Soc. 2018; 33(2): 671-676
Online first article January 9, 2018 Printed April 30, 2018
https://doi.org/10.4134/CKMS.c170221
Copyright © The Korean Mathematical Society.
C\^ong-Tr\`inh L\^e
Quy Nhon University
In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a \textit{generic class} of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial optimization problem for Morse polynomials has a finite convergence.
Keywords: gradient ideal, Milnor number, Morse polynomial, non-degener\-ate critical point, polynomial optimization
MSC numbers: Primary 14B05, 14H20, 11E25, 14P10, 90C22
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