Abstract: The object of the study is to solve the inverse problem of kinematics, as an optimization problem, under the conditions of a moving target. The subject of the study is the consideration of the drift of the objective function, as a result of the movement of the target, in the process of optimization. To solve the inverse problem of the kinematics of a multi-link manipulator, in the conditions of the time-varying position of the target, an effective algorithm for search optimization has been developed. Its essence consists in estimating the drift velocity, the formulated objective function, at each step of the search and taking into account the influence of the drift of the target when choosing the direction of the search. The modification of the method for the variable drift velocity of the objective function is considered. Estimates of the drift velocity are calculated by the recursive least squares method based on two modes: continuous search and search movement with repeated experiments at each vertex. The drift effect on the value of the objective function is obtained by integrating the drift velocity estimates on the time interval between the measurements. The author proposes a method for taking into account the drift of the objective function in the optimization problem. The proposed method showed its effectiveness in optimization problems with one and several extremums, using the example of simplex search and the genetic algorithm, operating under conditions of unstable drift of the objective function. The experimental limits of the effectiveness of the application of the method are determined experimentally.