Abstract
This chapter constructs the dual problems to the primary convex problems for ordinary discrete (DSI) and differential (DFI) inclusions. Duality theory, by virtue of the importance of its applications, is one of the central directions in optimal control theory. In mathematics and economics, duality theory is interpreted in the form of prices; in mechanics, potential energy and complementary energy are in a dual relationship—the displacement field and the stress field are solutions to the primary and dual problems, respectively. Besides these applications, duality often makes it possible to simplify the computational procedure and to construct a generalized solution to variational problems that do not have classical solutions. The duality theorems allow you to conclude that a sufficient condition for an extremum is an extremal relation for the primary and dual problems.
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