We establish necessary conditions of optimality for problems of optimal con
trol theory in the discrete time framework with infinite horizon. Our neces
sary conditions are in the form of Pontryagin principles. We treat smooth a
nd partially nonsmooth settings, without concavity. A strong motivation to
the study of such problems comes from dynamical macroeconomic theory, and t
here exist also some motivations provided by physics. (C) 2000 Academic Pre
ss.