Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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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.

A note on optimization with Morse polynomials

C\^ong-Tr\`inh L\^e

Quy Nhon University

Abstract

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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