Abstract

This chapter concerns deterministic and stochastic nonstationary discrete-time optimal control problems (OCPs) with an infinite horizon. We show, using Gâteaux differentials, that the so-called Euler equation (EE) and a transversality condition (TC) are necessary conditions for optimality. In particular, the TC is obtained in a more general form and under milder hypotheses than in previous works. Sufficient conditions are also provided. We find closed-form solutions to several (discounted) stationary and nonstationary control problems. The results in this chapter come from González–Sánchez and Hernández–Lerma [37].

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