Work

Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity

Year: 2023

Type: article

Abstract: . Let [Formula: see text] be the convex cone consisting of real [Formula: see text]-variate degree [Formula: see text] forms that are strictly positive on [Formula: see text]. We prove that the Lebesgue volume of the sublevel set [Formula: see text] of [Formula: see text] is a completely monotone function on [Formula: see text] and investigate the related properties. Furthermore, we provide (partial) characterization of forms whose sublevel sets have finite Lebesgue volume.

Source: SIAM Journal on Applied Algebra and Geometry

DOI: 10.1137/22m1502458

Authors: Khazhgali Kozhasov, Jean B. Lasserre

Institutions: Technische Universität Braunschweig, Centre National de la Recherche Scientifique, Laboratoire d'Analyse et d'Architecture des Systèmes, Université de Toulouse, Institut de Mathématiques de Toulouse

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Centre National de la Recherche Scientifique

Awards: Numerical Safety for Computer-Aided Proofs, Artificial and Natural Intelligence Toulouse Institute, G3010527862, G3879958799, G602161992