Stable sequential Kuhn-Tucker theorem in one-dimensional inverse problems of dielectric reflectometry

In this paper, a new approach in the theory of nonlinear ill-posed problems is applied to the statement of one-dimensional inverse scattering problems. The first problem is the problem of reflectometry subsurface analysis of one-dimensional permittivity inhomogeneities. The second is the problem of the synthesis of multilayer dielectric structures with a desired reflection spectrum.