Work

Nonnegative forms with sublevel sets of minimal volume

Year: 2020

Type: article

Abstract: We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms whose Gram matrix has bounded Frobenius or nuclear (or, more generally, p -Schatten) norm. These volume-minimizing properties of the Euclidean ball with respect to its representation (as a sublevel set of a form of fixed even degree) complement its numerous intrinsic geometric properties. We also provide a probabilistic interpretation of the results.

Source: Mathematical Programming

DOI: 10.1007/s10107-020-01584-0

Authors: Khazhgali Kozhasov, Jean Bernard 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: hybrid

Estimated APC paid: $2,740

Funders: European Commission, Horizon 2020