The zinc oxide rotary kiln, as an essential piece of equipment in the zinc smelting industrial process, is presenting new challenges in process control. China's strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry, including green production and the use of fewer resources; thus, traditional stability control is no longer suitable for multi-objective control tasks. Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics (CFD) simulation models to study its dynamics, these models cannot be directly applied to process control due to their high computational complexity. To address these issues, this paper proposes a multi-objective adaptive optimization model predictive control (MAO-MPC) method based on sparse identification. More specifically, with a large amount of data collected from a CFD model, a sparse regression problem is first formulated and solved to obtain a reduction model. Then, a two-layered control framework including real-time optimization (RTO) and model predictive control (MPC) is designed. In the RTO layer, an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up. By solving the optimization problem in real time, a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state. Our experiments show the strength and reliability of the proposed method, which reduces the usage of coal while maintaining high profits.