If the authors are able to find a local verification function associated with an admissible trajectory x(.), then x(.) is a local minimizer. It is of interest therefore to know when such local verification functions exist. In this paper it is shown that the existence of a local verification function is necessary for x(.) to be a local minimizer, under a normality hypothesis. The novelty of these results is that they treat problems with a general endpoint constraint and where the endtime is a choice variable. Here the value function of the original problem does not serve as a local verification function; instead it must be constructed from some derived problem. The data are allowed to be measurable in the time variable, and the normality hypothesis is expressed in terms of recent free-endtime necessary conditions of optimality for problems with measurable time dependence.
