  This paper is devoted to a study of infinite horizon optimal control problems
with time discounting and time averaging criteria in discrete time. It is known
that these problems are related to certain infinite-dimensional linear
programming problems, but compactness of the state constraint is a common
assumption imposed in analysis of these LP problems. In this paper, we consider
an unbounded state constraint and use Alexandroff compactification to carry out
the analysis. We also establish asymptotic relationships between the optimal
values of problems with time discounting and long-run average criteria.
