A heuristic approach to necessary conditions of optimality

Abstract

A simple, direct method is presented for deriving necessary conditions of optimality covering most of the situations encountered in practice. The method is based on the observation that, if generalized functions are admitted, a broad class of optimal control problems can be transcribed into a canonical form called the Canonical Variational Problem (CVP). The necessary optimality condition for CVP is phrased in the form of a Lagrange multiplier rule. This condition contains many of the results relating to minimum principles in the optimal control literature.