Non-linear optimal perturbations are defined here as those of minimum energy leading to subcritical instability. We show that a necessary condition for an initial perturbation to be a non-linear optimal is that the initial perturbation energy growth is zero. The fulfillment of this condition does not depend on the disturbance amplitude but only on the linearized operator as long as the non-linearity conserves energy. Saddle point solutions and linear optimal perturbations leading to maximum transient growth both satisfy the non-linear optimality condition. We discuss these issues on low-dimensional models of subcritical transition for which non-linear optimals and the minimum threshold energy are computed.