Generalized truncated moment problems with unbounded sets
Numerical Analysis
2022-08-02 v1 Numerical Analysis
Optimization and Control
Abstract
This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a convergent hierarchy of Moment-SOS relaxations for approximating these cones. With them, we give a Moment-SOS method for solving generalized truncated moment problems with unbounded sets. Finitely atomic representing measures, or certificates for their nonexistence, can be obtained by the proposed method. Numerical experiments and applications are also given.
Cite
@article{arxiv.2208.00354,
title = {Generalized truncated moment problems with unbounded sets},
author = {Lei Huang and Jiawang Nie and Ya-Xiang Yuan},
journal= {arXiv preprint arXiv:2208.00354},
year = {2022}
}