Tomas Bajbar – Optimization Online

Coercive polynomials: Stability, order of growth, and Newton polytopes

Published: 2015/10/13, Updated: 2018/01/19

Global Optimization Theory, Polyhedra coercivity, convenient polynomials, error bound, newton polytope, order of growth, stability

In this article we introduce a stability concept for the coercivity of multivariate polynomials $f \in \mathbb{R}[x]$. In particular, we consider perturbations of $f$ by polynomials up to the so-called degree of stable coercivity, and we analyze this stability concept in terms of the corresponding Newton polytopes at infinity. For coercive polynomials $f \in \mathbb{R}[x]$ … Read more

Coercive polynomials and their Newton polytopes

Published: 2014/08/02, Updated: 2015/08/07

Tomas Bajbar

Oliver Stein

Global Optimization Theory, Polyhedra coercivity, newton polytope, non-compact semi-algebraic sets, polynomial optimization

Many interesting properties of polynomials are closely related to the geometry of their Newton polytopes. In this article we analyze the coercivity on $\mathbb{R}^n$ of multivariate polynomials $f\in \mathbb{R}[x]$ in terms of their Newton polytopes. In fact, we introduce the broad class of so-called gem regular polynomials and characterize their coercivity via conditions imposed on … Read more