The sensitivity of the solution of some optimization problems with perturbation

We consider perturbed optimization problems that formally represent the problem of finding the extremum of functions of several variables that arise when applying the methods of linear convolution and an ideal point where some of the weight coefficients depend on a small parameter. On the basis of the asymptotic analysis of the problem, the sensitivity of the solution to the change of a small parameter is described, which makes it possible to construct a correction for the solution