Geodesic
Comparative analysis of numerical methods for solving problems of optimal control the behavior of economic agents in the conditions of competitiveness
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 2 (2013) no. 2, pp. 118-125

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In work the dynamic model of competitive behavior of the enterprises of cellular communication in the form of system of the differential equations with delay is offered. Numerical methods and algorithms for the solution of a problem of optimum control by behavior of mobile operators in the conditions of competitive fight for consumers of communication services are realized. The problem of optimum control by behavior of the enterprises of cellular communication with continuous delay with use of the principle of a maximum of Pontryagin for systems with continuous delay is formulated and solved. Conditions of an optimality for the solution of a problem of management are received by dynamics of development of subscriber base of firm No. 1. The method of linearization of system of the nonlinear differential equations with delay is realized and search of the optimum solution of a task by means of operations of improvement of the management, repeated in iterative procedure, on the example of modification of a method Shatrovsky is carried out.
Keywords: mathematical model, delay, optimum control, management improvement. 
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     title = {Comparative analysis of numerical methods for solving problems of optimal control the behavior of economic agents in the conditions of competitiveness},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
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I. P. Bolodurina; T. A. Ogurtsova; E. P. Maas. Comparative analysis of numerical methods for solving problems of optimal control the behavior of economic agents in the conditions of competitiveness. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 2 (2013) no. 2, pp. 118-125. http://geodesic.mathdoc.fr/item/VYURV_2013_2_2_a10/