An approach to the solution of discontinuous extremal problems (Q1913069)

An approach to the analysis of discontinuous functions and to the solution of discontinuous extremal problems is described. The approach is based on the so-called approximational gradient. This concept was introduced in the book ``Optimization of discontinuous functions'' (Russian) (1984; Zbl 0535.49001)] published by the author and \textit{L. A. Majboroda}. The approximational gradient is a vector generalizing the concept of subgradient, which is known from the literature. It is used to generalize the basic theorems from differential calculus and optimization (e.g., Fermat, Lagrange, Kuhn-Tucker, and Dubovitskij-Milyutin theorems as well as Pontryagin maximum principle). The author also generalizes the Newton-Kantorovich method for solving operator equations and includes results of some numerical experiments.