  Many steady-state problems in power systems, including rectangular
power-voltage formulations of optimal power flows in the alternating-current
model (ACOPF), can be cast as polynomial optimisation problems (POP). For a
POP, one can derive strong convex relaxations, or rather hierarchies of ever
stronger, but ever larger relaxations. We study means of switching from solving
the convex relaxation to Newton method working on a non-convex Lagrangian of
the POP.
