The Moment-SOS hierarchy
Optimization and Control
2018-08-13 v1
Abstract
The Moment-SOS hierarchy initially introduced in optimization in 2000, is based on the theory of the K-moment problem and its dual counterpart, polynomials that are positive on K. It turns out that this methodology can be also applied to solve problems with positivity constraints " f (x) 0 for all x K " and/or linear constraints on Borel measures. Such problems can be viewed as specific instances of the " Generalized Problem of Moments " (GPM) whose list of important applications in various domains is endless. We describe this methodology and outline some of its applications in various domains.
Keywords
Cite
@article{arxiv.1808.03446,
title = {The Moment-SOS hierarchy},
author = {Jean Lasserre},
journal= {arXiv preprint arXiv:1808.03446},
year = {2018}
}
Comments
To appear in Proceedings of ICM-2018, Rio de Janeiro