An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems. II. Applications

In this article the general necessary conditions for variational problems obtained in Part I are specialized to a number of particular problems. These problems include all of the important optimal control problems, both with and without restricted phase coordinates, problems arising from quasiconvex families of functions, and discrete optimal control problems of various types. The necessary conditions obtained include, as special cases, the Pontryagin maximum principle and its various extensions and generalizations, as well as the associated transversality conditions.