A Sublevel Moment-SOS Hierarchy for Polynomial Optimization

This paper is about a general polynomial optimization framework exploring sublevel sparsity, that can apply to sparse/dense problems, and has shown good performance compared to state-of-the-art sparse frameworks both in combinatorial optimization and deep learning. Previous work includes [Lasserre, 2001] which is the first paper introducing Lasserre’s SDP hierarchy for solving constrained and unconstrained POPs, [Lasserre, 2006], [Waki et al., 2005] which explore correlative sparsity in Lasserre’s hierarchy, and [Wang et al., 2019] which explores term sparsity in Lasserre’s hierarchy. [bib, link, code]