Differentiation functor and its application in the optimization control theory

Abstract

The differentiation of operators is defined as the functor from the category of Banach spaces with fixed points and germs of operators as morphisms to the category of Banach spaces with linear continuous operators. It is used for obtaining necessary conditions of optimality for abstract optimization control problems. Classical and extended operator derivatives are considered. An optimization control problem for a nonlinear elliptic equation is analyzed as an example.