  We establish necessary conditions of optimality for discrete-time
infinite-horizon optimal control in presence of constraints at infinity. These
necessary conditions are in form of weak and strong Pontryagin principles. We
use a functional analytic framework and multipliers rules in Banach (sequence)
spaces. We establish new properties on Nemytskii operators in sequence spaces.
We also provide sufficient conditions of optimality. MSC 2010: 49J21, 65K05,
39A99.
