On the Euler equation approach to discrete--time nonstationary optimal control problems

Abstract

We are concerned with deterministic and stochastic nonstationary discrete--time optimal control problems in infinite horizon. We show, using Gâteaux differentials, that the so--called Euler equation and a transversality condition are necessary conditions for optimality. In particular, the transversality condition is obtained in a more general form and under milder hypotheses than in previous works. Sufficient conditions are also provided. We also find closed--form solutions to several (discounted) stationary and nonstationary control problems.