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We address optimization of the spin current intensity profile needed to achieve spin torque switching of a nanomagnet. For systems with Ohmic dissipation we prove that the optimal current drives the magnetization along the trajectory, which is exact time-reversed replica of the relaxation trajectory toward the equilibrium. In practice it means that the optimal current is very nearly twice the minimal critical current needed to switch the magnet. Pulse duration of such an optimal current is a slow logarithmic function of temperature and the required probability of switching.