Systematic and fast switching for the purposes of reducing losses in power transmission networks is treated as an optimization problem whereby switching is to be understood in a general and comprehensive way. Injected currents applied to a base network are used to model the switching operation. These currents are used as variables in a linear programming (LP) problem formulation. The objective function, i.e. the change in losses, can be expressed by the injected currents, taking into account that all nodes are constrained by constant active powers except for the slack node. The change of power of the slack node is the change in losses, which is obtained by a two-step approximation. Each single optimal switching operation is obtained by an LP-like operation followed by a load-flow update. The interaction between LP and AC load-flow leads to a sequence of optimal switching operations whereby losses are reduced to a minimum subject to the given constraints. >