Gradient methods for nonstationary unconstrained optimization problems

Problems of unconstrained optimization with an objective function depending on a scalar parameter (time) are considered. The solution of these problems also depends on time and any numerical method must keep track of this dependence. For the solution of such nonstationary problems, a discrete gradient method is treated, in which only one gradient step is taken for the varying function at each instant of time. Estimates of intervals (variations) between exact and approximate solutions are found and an asymptotic behavior of these estimates is defined.