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We establish necessary conditions of optimality for discrete-timeinfinite-horizon optimal control in presence of constraints at infinity. Thesenecessary conditions are in form of weak and strong Pontryagin principles. Weuse 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.

Pontryagin Principles in Infinite Horizon in Presence of Asymptotical Constraints