Functions Optimization

Abstract

This chapter presents a number of concepts and methods of differential calculus which are important by themselves, being, however, applicable both in variational calculus and in optimal control theory. Only the case of functions of real variables is considered here. Natural and exact sciences are based on functional relationships between different variables. If these functional relationships meet certain criteria, they can be studied by using procedures developed and systematized under the framework of ordinary differential and integral calculus. In essence, these procedures allow emphasizing properties common to many types of functions such as continuity, monotony or differentiability. This chapter reminds a number of concepts and methods of differential calculus which are important by themselves, being, however, applicable both in variational calculus and in optimal control theory (Forray 1975). Only the case of functions of real variables is considered here.