On the existence of an optimal solution of the epsilon variational problem

It has been shown that known sufficient conditions for existence of optimal control imply existence of an optimal solution of the nondynamic epsilon variational problem as formulated by Balakrishnan.This work forms a part of the doctoral dissertation submitted by the author in early 1969 at UCLA and was supported in part by the Air Force Office of Scientific Research under Grant No. 69–1646. The author expresses his gratitude to Professor A. V. Balakrishnan for many useful discussions in the preparation of this work.