Geodesic
Solution of nondifferentiable optimization problem for object with distributed parameters based on quasi-asymptotic approximate model
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 118-124.

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The possibility of approximate quasi-asymptotic models application is considered on an example of the solution of a time-optimal heating problem. To solve an optimal control problem the numerical algorithm has been used on the basis of spline extrapolation of the minimized field at each iteration. It is shown that this approach to the time-optimal control problem can provide with negligible error the determination of maximum admissible accuracy and interval durations for one-, two-, and three- stage control.
Keywords: time-optimal problem, quasi-asymptotic model of heating process, error of model, problem of nondifferentiable optimization, spline approximation method. 
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N. V. Diligenskiy; A. P. Efimov. Solution of nondifferentiable optimization problem for object with distributed parameters based on quasi-asymptotic approximate model. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 118-124. http://geodesic.mathdoc.fr/item/VSGTU_2011_4_a14/

[1] Rapoport É. Ya., Process optimization of induction heating of metal, Metallurgiya, Moscow, 1993, 279 pp.

[2] Rapoport É. Ya., The alternance method in applied problems of optimization, Nauka, Moscow, 2000, 336 pp. | Zbl

[3] Efimov A. P., “A method for constructing a uniformly suitable approximation of nonstationary heat conduction problems solutions in finite dimensions bodies”, Vestn. Sam. Gos. Tekhn. Un-ta. Ser. Tekhn. Nauki, 2008, no. 2(22), 196–200

[4] Diligenskiy N. V., Efimov A. P., “Using the principle of subsidiarity for the design of systems of mathematical models for heat conduction problems with the required approximation properties”, Proceedings of the Third Russian National Conference on Heat Transfer, v. 7, MÉI, Moscow, 2002, 111–114

[5] Efimov A. P., “Spline extrapolation algorithm for solving semi-infinite optimization”, Vestn. Sam. Gos. Tekhn. Un-ta. Ser. Tekhn. Nauki, 2009, no. 2(24), 25–32

[6] Efimov A. P., “Application of spline extrapolation algorithm for solving semi-infinite optimization”, Vestn. Sam. Gos. Tekhn. Un-ta. Ser. Tekhn. Nauki, 2010, no. 2(26), 44–51