The Pontryagin maximum principle for optimal control problem with an asymptotic endpoint constraint

Infinite-horizon optimal control problems with asymptotic endpoint constraints naturally arise in economics in studies of growth processes. A new version of the Pontryagin maximum principle for problems of this type is in the focus of the presentation. The result is obtained without any a priory assumptions on asymptotic behavior of the optimal trajectory. The proof is based on reducing the original problem to a family of standard finite-horizon problems with increasing terminal times and exploitation of properties of the conditional cost function.