Publications
Article · SIAM Journal on Applied Algebra and Geometry · November 29, 2023
Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity
Khazhgali Kozhasov, Jean Bernard Lasserre
Abstract
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.
Advanced Optimization Algorithms ResearchMathematical Inequalities and ApplicationsAdvanced Combinatorial Mathematicssublevel setscomplete monotonicityconvex cones
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