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1996-1997 | 24 | 2 | 141-147
Tytuł artykułu

The gradient projection method for solving an optimal control problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
Rocznik
Tom
24
Numer
2
Strony
141-147
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-08-18
poprawiono
1996-02-16
Twórcy
autor
  • Department of Mathematics, Faculty of Science, Minia University Minia, Egypt
Bibliografia
  • [1] A. G. Butkovskiĭ, Optimal Control Theory for Systems with Distributed Parameters, Nauka, Moscow, 1965 (in Russian).
  • [2] Yn. V. Egorov, On some optimal control problems, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963), 887-904 (in Russian).
  • [2] M. H. Farag, A numerical solution to a nonlinear problem of the identification of the characteristics of a mathematical model of heat exchange, in: Mathematical Modeling and Automated Systems, A. D. Iskenderov (ed.), Bakin. Gos. Univ., Baku, 1990, 23-30 (in Russian).
  • [4] M. H. Farag and S. H. Farag, An existence and uniqueness theorem for one optimal control problem, Period. Math. Hungar. 30 (1995), 61-65.
  • [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  • [6] A. D. Iskenderov, On a certain inverse problem for quasilinear parabolic equations, Differentsial'nye Uravneniya 10 (1974), 890-898 (in Russian).
  • [7] A. D. Iskenderov and R. K. Tagiev, Optimization problems with controls in coefficients of parabolic equations, ibid. 19 (1983), 1324-1334 (in Russian).
  • [8] J.-L. Lions, Control problems in systems described by partial differential equations, in: Mathematical Theory of Control, A. V. Balakrishnan and L. W. Neustadt (eds.), Academic Press, New York and London, 1969, 251-271.
  • [9] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian).
  • [10] K. A. Lurie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian).
  • [11] M. D. Madatov, Regularization of one class of optimal control problems, in: Approximate Methods and Computer, A. D. Iskenderov (ed.), Bakin. Gos. Univ., Baku, 1982, 78-80 (in Russian).
  • [12] A. Mokrane, An existence result via penalty method for some nonlinear parabolic unilateral problems, Boll. Un. Mat. Ital. B 8 (1994), 405-417.
  • [13] G. A. Phillipson and S. K. Mitter, Numerical solution of a distributed identification problem via a direct method, in: Computing Methods in Optimization Problems-2, L. A. Zadeh, L. W. Neustadt and A. V. Balakrishnan (eds.), Academic Press, New York, 1969, 305-315.
  • [14] E. Polak, Computational Methods in Optimization, Academic Press, New York, 1971.
  • [15] B. N. Pshenichnyĭ and Yu. M. Danilin, Numerical Methods in Extremal Problems, Mir, Moscow, 1982.
  • [16] J. B. Rosen, The gradient projection method for nonlinear programming. Part I: Linear constraints, SIAM J. Appl. Math. 8 (1960), 181-217.
  • [17] J. B. Rosen, The gradient projection method for nonlinear programming. Part II: Nonlinear constraints, ibid. 9 (1961), 514-532.
  • [18] Ts. Tsachev, Optimal control of linear parabolic equation: The constrained right-hand side as control function, Numer. Funct. Anal. Optim. 13 (1992), 369-380.
  • [19] F. P. Vasil'ev, Numerical Methods for Solving Extremal Problems, Nauka, Moscow, 1988 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i2p141bwm
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