Solution of a simplified advertising model using optimal control techniques

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Keywords:

advertising model, optimal control, concentrated parameters, Pontryagin maximum principle.

Abstract

In this article we present a simplification of the distributed model of advertising by formulating it as a family of optimal control problems with concentrated parameters. We consider two simplified models: linear and non-linear. Linear model is solved analytically using the maximum principle. To solve non-linear model, we construct a numerical algorithm based on two nonconventional increment formulae for the objective functional.

MSC : 49N05

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Author Biographies

  • Ekaterina Tuchnolobova, Universidad Estatal de Irkutsk, Irkutsk.
    Licenciada en Economía Matemática, estudiante de doctorado
  • O Vasilieva, Universidad del Valle

    PhD in Engineering, PhD in Physical Sciences and Mathematics.

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References

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G. Feightinger, R. F. Hartl and S. Sethi. Dynamic optimal control models in advertising: recent developments. Management Science, ISSN 0025-1909, 40(2), 195-226 (1994).

S. Sethi. Dynamic optimal control models in advertising: a survey.SIAM Review, ISSN 0036-1445, 19(4), 685-725 (1977).

V. A. Srochko and N. V.Mamonova. Iterative procedures for solving optimal control problems based on quasigradient approximations . Russian Mathematics (Iz. Vuz), ISSN 1066-369X, 45(12), 52-64 (2001).

V. A. Srochko.Modernization of gradient-type methods in optimal control problems. Russian Mathematics (Iz. Vuz), ISSN 1066-369X, 46(12), 64-76 (2002).

O. V. Vasiliev. Optimization methods.World Federation Publishers Company, 1996, ISBN 1885978243.

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Issue

Vol. 7 No. 13 (2011)

Section

Articles

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How to Cite

Tuchnolobova, E., Terletskii, V., & Vasilieva, O. (2011). Solution of a simplified advertising model using optimal control techniques. Ingeniería Y Ciencia, 7(13), 161-183. https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/406

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