Extremal problems for discrete and differential inclusions of hyperbolic type with distributed parameters
A system of discrete convex inclusions is considered. The system is called hyperbolic since it can be viewed as a finite difference approximation of a boundary value problem for the second order hyperbolic inclusions. For this system a convex extremal problem is considered. Using Pshenichny's concept of locally adjoint mappings, sufficient and necessary conditions of optimality are derived. Passing formally to the limit with the step of discretization, some conditions are obtained, which are shown to be sufficient optimality conditions for the discretized hyperbolic extremal problem.
sufficient and necessary conditions of optimality
scientific article; zbMATH DE number 4198903