A Fine-Grained Variant of the Hierarchy of Lasserre
This work addresses computational bottlenecks in convex optimisation for researchers and practitioners, though it appears incremental as it builds on existing hierarchies.
The paper tackles the challenge of solving higher levels in the Lasserre hierarchy for polynomial optimisation problems, which are computationally intensive, by introducing a fine-grained variant and first-order methods that enable efficient warm-starting from lower levels.
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.