This paper explores the multiple local characteristics of the RAE2822 in the process of minimising drag optimization. AIAA Aerodynamic Design Optimization Discussion Group(ADODG) case 2 is used. The airfoil is parameterized by using the FFD (free-form deform) parameterization technique, and the initial perturbation is added to the airfoil by using the uniform latin hypercube method. Then the gradient-based optimization algorithm is used to optimize the airfoil after different disturbances, and the optimization results are compared with the optimization results of the global optimization algorithm. The results show that ADODG case2 is a convex peak design problem. The gradient-based algorithm can obtain a relatively satisfactory optimal solution and has a higher optimization efficiency. The conclusion can be inferred from this study that airfoil transonic minimising drag optimization subject to area constraint is possible a convex peak design problem. Gradient optimization algorithms can be used directly.