Generalized predictive control (GPC) is an attractive predictive control formulation, the major weakness of which has been the lack of general stability guarantees. As a result, different variants of the method have been proposed which yield stabilizing control. Most of these however rely on the addition to the control objective of a set of equality constraints which sub-optimally restricts the class of inputs considered in the optimization of performance. On the other hand, the use of an infinite costing horizon is known to lead naturally to stability but has not been popular due to implementation difficulties. It has indeed not been clear how to minimize GPC-type costs, in the constrained case, when an infinite costing horizon is used. This paper presents a practical means of implementing GPC with an infinite costing horizon with and without inequality constraints.