Dorroh, J. R.; Ferreyra, G. Optimal advertising in exponentially decaying markets. (English) Zbl 0797.90055 J. Optimization Theory Appl. 79, No. 2, 219-236 (1993). Summary: 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. Cited in 2 Documents MSC: 90B60 Marketing, advertising 49L20 Dynamic programming in optimal control and differential games 49N25 Impulsive optimal control problems 93C95 Application models in control theory Keywords:optimal advertising singular control problem; unbounded control; reparametrization; impulsive control PDFBibTeX XMLCite \textit{J. R. Dorroh} and \textit{G. Ferreyra}, J. Optim. Theory Appl. 79, No. 2, 219--236 (1993; Zbl 0797.90055) Full Text: DOI References: [1] Vidale, M. L., andWolfe, H. B.,An Operations Research Study of Sales Response to Advertising, Operations Research, Vol. 5, pp. 370-381, 1957. · doi:10.1287/opre.5.3.370 [2] Sethi, S. P.,Optimal Control of the Vidale-Wolfe Model, Operations Research, Vol. 21, pp. 998-1013, 1973. · Zbl 0278.49007 · doi:10.1287/opre.21.4.998 [3] Dorroh, J. R., andFerreyra, G.,A Multi-State, Multi-Control Problem with Unbounded Controls, to appear in SIAM Journal on Control and Optimization. [4] Miele, A.,Problemi di Minimo Tempo nel Volo Non-Stazionario degli Aeroplani, Atti della Accademia delle Scienze di Torino, Vol. 85, pp. 41-52, 1950-51. [5] Ferreyra, G.,The Optimal Control Problem for the Vidale - Wolfe Advertising Model Revisited, Optimal Control Applications and Methods, Vol. 11, pp. 363-368, 1990. · Zbl 0726.90039 · doi:10.1002/oca.4660110407 [6] Sussmann, H. J.,Semigroup Representations, Bilinear Approximation of Input-Output Maps, and Generalized Inputs, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, Germany, Vol. 131, pp. 172-191, 1976. · Zbl 0353.93025 [7] Sussmann, H. J.,On the Gap between Deterministic and Stochastic Differential Equations, Annals of Probability, Vol. 6, pp. 19-42, 1978. · Zbl 0391.60056 · doi:10.1214/aop/1176995608 [8] Sethi, S. P.,Dynamic Optimal Control Models in Advertising: A Survey, SIAM Review, Vol. 19, pp. 685-725, 1977. · Zbl 0382.49001 · doi:10.1137/1019106 [9] Sethi, S. P., andTaksar, M. I.,Deterministic Equivalent for a Continuous-Time Linear-Convex Stochastic Control Problem, Journal of Optimization Theory and Applications, Vol. 64, pp. 169-181, 1990. · Zbl 0687.93081 · doi:10.1007/BF00940030 [10] Bressan, A., andRampazzo, F.,On Differential Systems with Vector-Valued Impulsive Controls, Bollettino della Unione Matematica Italiana, Serie B, Vol. 3, pp. 641-656, 1988. · Zbl 0653.49002 [11] Bolza, O.,Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946. · JFM 35.0373.01 [12] Fleming, W. H., andRishel, R. W.,Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, New York, 1975. · Zbl 0323.49001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.