Abstract
An optimal advertising singular control problem with unbounded control is formulated in a generalized fashion by introducing a reparametrization of time. This reparametrization is a new control. The method of dynamic programming is then used to determine the optimal synthesis. Afterward, it is easy to drop the reparametrization of time. In this interpretation, the synthesis shows an impulsive control at the initial time.
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Communicated by R. Rishel
The research of the second author was partially supported by Louisiana Education Quality Support Fund, Grant No. 86-LBR-016-04.
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Dorroh, J.R., Ferreyra, G. Optimal advertising in exponentially decaying markets. J Optim Theory Appl 79, 219–236 (1993). https://doi.org/10.1007/BF00940579
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DOI: https://doi.org/10.1007/BF00940579