We establish conditions under which a sequence of finite horizon convex programs monotonically increases in value to the value of the infinite program; a subsequence of optimal solutions converges to the optimal solution of the infinite problem. If the conditions we impose fail, then (roughtly) the optimal value of the infinite horizon problem is an improper convex function. Under more restrictive conditions we establish the necessary and sufficient conditions for optimality. This constructive procedure gives us a way to solve the infinite (long range) problem by solving a finite (short range) problem. It appears to work well in practice.