An increase in the share of weather-dependent generation at low voltage levels necessitates incorporating the low-voltage network in optimizing a distribution network. Optimization in a multi-voltage network requires significant computation time and effort due to many nodes operating at different voltage levels. This research proposes a decomposition and strategic optimization method to reduce the computation requirements for such large multi-voltage distribution networks. The proposed algorithm reduces the space complexity and the computation time required for solving the optimization routines of these multi-voltage distribution networks. A virtual transformer model incorporates tap-changer as a continuous variable in the semidefinite programming power flow optimization model. The zero-duality gap condition for multiple virtual transformers is proven empirically. Compared to a centralized optimization using the same power flow model, the proposed framework reduced the computation time by 96%.