  The alternating-current optimal power flow (ACOPF) is one of the best known
non-convex non-linear optimisation problems. We present a novel re-formulation
of ACOPF, which is based on lifting the rectangular power-voltage
rank-constrained formulation, and makes it possible to derive alternative SDP
relaxations. For those, we develop a first-order method based on the parallel
coordinate descent with a novel closed-form step based on roots of cubic
polynomials.
