Abstract In order to improve the ability of no-search mathematical programming under limit analysis, and guide big data to optimize classification, a non-search mathematical programming model based on limit analysis model is proposed. The non-search mathematical programming of hyperbolic differential equations in the limit analysis model is analyzed, which provides a mathematical theoretical basis for solving the stability control problem of the system. The hyperbolic differential equation is constructed and the characteristic decomposition of the linear programming model is carried out by using adaptive limit analysis method. The searching delay two-degree-of-freedom control method is used at the load balancing point to adaptively optimize the searching delay parameters of the limit analysis model. In this paper, the hyperbolic differential equations in the limit analysis model are obtained, and the theorems of non-search mathematical programming are given. The mathematical analysis shows that the hyperbolic differential equations in the limit analysis model have the characteristics of non-search mathematical programming. The given theorem of non-search mathematical programming is reliable, and the characteristic solutions of differential equations are stable convergence, which can guide the stability control and improve the control accuracy and reliability. The simulation results show that the algorithm has better convergence and shorter time cost under the limit analysis.