A note on optimization with Morse polynomials

TL;DR

This paper proves that the gradient ideal of Morse polynomials is radical, leading to finite convergence in unconstrained polynomial optimization problems for this class.

Contribution

It establishes that Morse polynomials have radical gradient ideals, providing a new class of polynomials with this property and confirming finite convergence in optimization.

Findings

Gradient ideal of Morse polynomial is radical

Finite convergence for optimization problems involving Morse polynomials

Reconfirmation of previous results on Morse polynomial optimization

Abstract

In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a 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.