Volume Of Sub-level Sets Of Homogeneous Polynomials
Optimization and Control
2018-10-25 v1
Abstract
Consider the sub level set K := {x : g(x) 1} where g is a positive and homogeneous polynomial. We show that its Lebesgue volume can be approximated as closely as desired by solving a sequence of generalized eigenvalue problems with respect to a pair of Hankel matrices of increasing size, and whose entries are obtained in closed form.
Keywords
Cite
@article{arxiv.1810.10224,
title = {Volume Of Sub-level Sets Of Homogeneous Polynomials},
author = {Jean Lasserre},
journal= {arXiv preprint arXiv:1810.10224},
year = {2018}
}