6 - Optimization of Discrete and Differential Inclusions with Distributed Parameters via Approximation

Abstract

This chapter is devoted to an investigation of problems described by the so-called discrete and differential inclusions with distributed parameters. The past decade has seen an ever more intensive development of the theory of extremal problems involving multivalue mappings with distributed parameters. A great many problems in economic dynamics, as well as classical problems on optimal control in vibrations, chemical, engineering, heat, diffusion processes, differential games, and so on, can be reduced to such investigations. The results one wishes to obtain fall into four categories: necessary and sufficient conditions for discrete inclusions, optimization of the corresponding discrete-approximation problems, sufficient conditions for partial differential inclusions, and the construction of duality relations. In addition to many works devoted to optimization of partial differential inclusions, the qualitative problems for boundary-value problems for systems of first-order partial differential inclusions are considered.