On Necessary Optimality Conditions for Ramsey-Type Problems

Abstract

We study an optimal control problem in infinite time, where the integrand does not depend explicitly on the state variable. A special case of such problem is the Ramsey optimal capital accumulation in centralized economy. To complete the optimality conditions of Pontryagin's maximum principle, so called transversality conditions of different types are used in the literature. Here, instead of a transversality condition, an additional maximum condition is considered.

On a sufficient condition for infinite horizon optimal control problems

“…This sufficient condition is yet to be studied. Necessary conditions for this problem are considered in Belyakov (2019).…”