Global Solution of the Clustering Problem via Graph Theoretical Approach

In this article we consider clustering problems which we model as a non-convex continuous minimization problem with the maximum norm representing the distance measure. We then reformulate this continuous problem in light of graph theoretical instances which enables us to construct a bisection algorithm converging to the globally minimal value of the original clustering problem … Read more

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

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

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