English

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) \le 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}
}