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Large horsepower induction motors play a critical role in the operation of industrial facilities. In this respect, the distribution network operators dedicate a high priority to the operational safety of these motor loads. In this paper, the induction motor starting is modeled analytically and in a semi-static fashion. This model is imbedded in a convex distribution system restoration problem. In this optimization problem, it is aimed to determine the optimal status of static loads and the optimal dispatch of distributed generators such that: a) the induction motors can be reaccelerated in a safe way and, b) the total power of static loads that cannot be supplied before the motor energization, is minimized. The proposed optimization problem is applied in the case of a distribution network under different simulation scenarios. The feasibility and accuracy of the obtained results are validated using a) off-line time-domain simulations, and b) Power Hardware-In-the-Loop experiments.