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Optimal distributed dynamic advertising | | Carlo Marinelli
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22 Jun 2004 | | Subject: | Optimization and Control MSC-class: 90B60; 91B72; 49K27; 93C25 | math.OC | | Abstract: | We extend the classical dynamic advertising model of M. Nerlove and J.K. Arrow (1962) 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. | | Source: | arXiv, math.OC/0406435 | | Services: | Forum | Review | PDF | Favorites | |
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