A logarithmic advertising model is posed and solved for an optimal dynamic advertising policy for both finite and infinite horizon cases by using optimal control theory. In the case of the infinite horizon, the optimal long-run stationary equilibrium rate of advertising is obtained. It is shown...

Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state...