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The power flow equations model the relationship between voltages phasors and power flows and are therefore at the heart of many optimization and control problems relevant to electric power systems. The nonlinearity of the power flow equations results in a variety of algorithmic and theoretical challenges, including non-convex feasible spaces for optimization problems constrained by these equations. Using two new algorithms, this presentation illustrates and characterizes challenging non-convex feasible spaces associated with power system optimization problems. This presentation then describes a recent continuation-based algorithm that finds multiple local optima for the optimal power flow problem. Host: Hassan Hijazi |