Problems in power systems modelling alternating-current transmission constraints are non-convex, but of a great and growing importance in practice. We have shown [IEEE T. Power Systems, 31(1): 539–546] that one can construct a hierarchy of convexifications, whose optima converge to the global optimum of the non-convex problem. We have also developed custom first- and second-order methods for solving such convexifications. The first-order methods have trivial per-iteration time and memory requirements, but their rates of convergence limit their direct application to large instances. We have hence also introduced methods for switching from solving the convexification (e.g., using the first-order methods) to (any second-order methods on) the non-convex problem, once guarantees of converging to the same optimum are available. This allows one to tackle large-scale instances in practice and to guarantee global convergence in theory.
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