In the article the mathematical model and the technique of the accelerated optimization estimation of the main technical characteristics of the passenger aerial ropeway (step and height of intermediate supports, tension force of the bearing ropes) are developed. To calculate the optimal values of these technical characteristics, the task of technical and economic optimization was previously developed. The optimization task was based on the minimization of the objective function — the cost of the aerial ropeway construction, taking into account a number of structural constraints. The accelerated optimization estimate is based on the fact that the position of the minimum point of the objective function should be searched along the line of one of the mentioned constraints – constraint on the minimum of tension force of the bearing ropes. This allowed us to propose two ways of accelerated optimization evaluation: 1) reduction of the dimension of the optimization problem; 2) replacement of the search for the minimum of the objective function by the solution of a nonlinear algebraic equation. The proposed algorithm of accelerated optimization evaluation of the main technical characteristics of the passenger aerial ropeway allows to obtain exactly the same values as the result of solving the previously developed problem of technical and economic optimization, but with the use of more simple mathematical methods.