Reducing the operating energy costs of commercial buildings is an important problem faced by the facility managers. Additionally, energy cost from heating-ventilation-air-conditioners (HVAC) is a significant fraction (often greater than 50%) of the overall operational cost of these buildings. In this paper, we propose a pre-cooling framework that uses a 'gray box' thermal model of a building to compute the optimal set-point temperature schedules to minimize the operational cost of the HVACs. We also propose a technique which involves relaxing the non-linear constraint to improve the computational complexity of the optimization framework. This optimization framework is tested using data obtained from the building management system (BMS) of a commercial building in Australia. The optimal scheduling of the set-point temperatures results in peak power reduction by over 40% and energy bills by 25% to 30%. Furthermore, the relaxation of the non-linearity reduces the computation time approximately by a factor of 50 while resulting in only a negligible loss in optimality of about 2%. Reduction in computation time of the optimization increases its amenability to use this framework alongside existing BMS systems.