Motivated by the interest in modeling real-world systems as mixed logical dynamical (MLD) systems with signal temporal logic (STL) specifications, this paper introduces an efficient iterative optimization scheme for this class of systems. We focus on a microgrid system with energy losses, providing two formulations: a mixed-integer-based model and a model tailored to the proposed technique. A numerical case study using model predictive control (MPC) demonstrates that the proposed method significantly improves computation time compared to the classical mixed-integer linear programming (MILP) approach for longer time horizons, while also addressing discontinuity and volatility issues sometimes observed in the MILP approach.