Proof of the Maximum Principle

Abstract

This chapter is devoted to the proof of the maximum principle, Theorem V.3.1. We shall actually prove a theorem that is more general than the maximum principle and shall obtain the maximum principle as a special case of this theorem. An essential property of an optimal trajectory is used to motivate the introduction of a concept called ℱ-N extremality. A necessary condition for ℱ-N extremality is then stated (Theorem 3.1 of this chapter), and it is shown how this implies Theorem V.3.1.