Multi-dimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging multidimensional problems of nonstationary optimization, it is suggested to use a stochastic approximation algorithm (like SPSA) with perturbed input and constant step-size which has simple form. We get a finite bound of residual between estimates and time-varying unknown parameters when observations are made under an unknown but bounded noise. Applications of the algorithm are considered for a random walk, an optimization of UAV's flight, and a load balancing problem.