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

Hybrid Methods in Solving Alternating-Current Optimal Power Flows