English

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) \ge 0 for all x \in 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

R2 v1 2026-06-23T03:29:43.154Z