The paper presents a control variables optimization study for an airborne wind energy production system. The system comprises an airborne module in the form of a buoyant, rotating cylinder, whose rotation in a wind stream induces the Magnus effect-based aerodynamic lift. Through a tether, the airborne module first drives the generator fixed on the ground, and then the generator becomes a motor that lowers the airborne module. The optimization is aimed at maximizing the average power produced at the generator during a continuously repeatable operating cycle. The control variables are the generator-side rope force and the cylinder rotation speed. The optimization is based on a multi-phase problem formulation, where operation is divided into ascending and descending phases, with free boundary conditions and free cycle duration. The presented simulation results show that significant power increase can be achieved by using the obtained optimal operating cycle instead of the initial, empirically based operation control strategy. A brief analysis is also given to provide a physical interpretation of the optimal cycle results.