We study the problem of heating, ventilation and air conditioning (HVAC) control in a typical commercial building. We propose a model predictive control (MPC) approach which minimizes energy cost while satisfying occupant comfort and control actuator constraints, using a simplified system model and incorporating predictions of future weather and occupancy inputs. In simplified physics-based models of HVAC systems, the product between air temperatures and flow rates arising from energy balance equations leads to a non-convex MPC problem. Fast computational techniques for solving non-convex optimization can only provide certificates of local optimality. Local optima can potentially cause MPC to have worse performance than existing control implementations, so deserve careful consideration. The objective of this article is to investigate the phenomenon of local optima in the MPC optimization problem for a simple HVAC system model. In the first part of the article, simplified physics-based models and MPC desig...