Application of Pontryagin's principle of maximum to the inverse problems of scattering

We are concerned with the practical application of a new approach to the inverse problems of electromagnetic wave scattering. Our main goal is retrieval of an unknown permittivity distribution. Within the framework of such a statement the problem is reduced to minimization of some smoothing functional. Further minimization is carried out with the use of Pontryagin's (1983) principle of maximum, instead of approaches which are based on the Newton-Kantorovich iterative technique and Euler's equations.