A Fine-Grained Variant of the Hierarchy of Lasserre

Abstract

There has been much recent interest in hierarchies of progressively stronger convexifications of polynomial optimisation problems (POP). These often converge to the global optimum of the POP, asymptotically, but prove challenging to solve beyond the first level in the hierarchy for modest instances. We present a finer-grained variant of the Lasserre hierarchy, together with first-order methods for solving the convexifications, which allow for efficient warm-starting with solutions from lower levels in the hierarchy.

Partial Lasserre relaxation for sparse Max-Cut

“…This is an interesting question for future work. In particular, multilevel techniques like the ones used in Campos and Parpas (2018), Campos et al (2019), Ma et al (2019) can be useful in this context.…”