arXiv:2611.07777v1 Announce Type: cross Abstract: Heating, ventilation, and air-conditioning (HVAC) systems account for a significant portion of buildings' energy consumption, motivating the design of energy- and cost-efficient control strategies. However, conventional strategies employ simple, reactive control, without incorporating a model. Therefore, in this paper we adopt an economic model predictive control framework and focus on designing online algorithms to solve the control input design problems with a limited computational budget. In particular, we propose two tailored online algorithms based on projected gradient descent, with a custom projection routine, and the projected primal-dual method. We discuss the pros and cons of both algorithm designs, focusing in particular on computational efficiency. We further compare them through numerical experiments simulating the control of an HVAC system over the course of a day. The results show that computationally efficient online solvers for HVAC systems control are indeed possible. Moreover, the performance closely matches that of a baseline algorithm with unlimited computational budget, in terms of reference temperature tracking and comfort temperature range enforcement.