2025/01/04 by Papri Dey, Dey, Papri
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2501.02375
openalex publication_date 2025/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the class of \K-Lorentzian polynomials, a generalization of the distinguished class of Lorentzian polynomials. As shown in \citeGPlorentzian, the set of \K-Lorentzian polynomials is equivalent to the set of \K-completely log-concave (aka \K-CLC) forms. Throughout this paper, we interchangeably use the terms \K-Lorentzian polynomials for the homogeneous setting and \K-CLC polynomials for the non-homogeneous setting. By introducing an alternative definition of \K-CLC polynomials through univariate restrictions, we establish that any strictly \K-CLC polynomial of degree d ≤ 4 is Hurwitz-stable polynomial over \K. Additionally, we characterize the conditions under which a strictly \K-CLC of degree d ≥ 5 is Hurwitz-stable over \K. Furthermore, we associate the largest possible proper cone, denoted by \K(f,v), with a given \K-Lorentzian polynomial f in the direction v ∈ \inter \K. Finally, we investigate applications of \K-CLC polynomials in the stability analysis of evolution variational inequalities (EVI) dynamical systems governed by differential equations and inequality constraints.