Optimal Distributed Dynamic Advertisement
نویسنده
چکیده
We extend the classical dynamic advertising model of M. Nerlove and J. Arrow [11] adding a spatial dimension. We consider the general mixed problem of maximizing a utility function of product image at a fixed time and minimizing the corresponding cumulative cost of advertising. After an abstract treatment allowing for general utility and cost functions, as well as state and control constraints, we give a more explicit (although in general only suboptimal) solution of the problem through the linear-quadratic regulator in infinite dimensions. We also study, by similar methods, the problem of reaching a target level of awareness of the advertised product by a given deadline.
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