Large horsepower induction motors play a critical role as industrial drives in production facilities. The operational safety of distribution networks during the starting transients of these motor loads is a critical concern for the operators. In this paper, an analytical and convex optimization model is derived representing the starting transients of the induction motor in a semi-static fashion. This model is used to find the optimal energization sequence of different loads (static and motor loads) following an outage in a distribution network. The optimization problem includes the optimal control of the converter-based DGs and autotransformers that are used for the induction motor starting. These models together with the semi-static model of the induction motor are integrated into a relaxed power flow formulation resulting in a Mixed-Integer Second Order Cone Programming (SOCP) problem. This formulation represents the transient operational limits that are imposed by different protection devices both in the motor side and network side. The functionality of the proposed optimization problem is evaluated in the case of a large-scale test study and under different simulation scenarios. The feasibility and accuracy of the optimization results are validated using I) off-line time-domain simulations, and II) a Power Hardware-In-the-Loop experiment.