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.
@article{bwmeta1.element.bwnjournal-article-zmv24i2p141bwm,
author = {M. Farag},
title = {The gradient projection method for solving an optimal control problem},
journal = {Applicationes Mathematicae},
volume = {24},
year = {1997},
pages = {141-147},
zbl = {0871.49006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv24i2p141bwm}
}
Farag, M. The gradient projection method for solving an optimal control problem. Applicationes Mathematicae, Tome 24 (1997) pp. 141-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i2p141bwm/
[000] [1] A. G. Butkovskiĭ, Optimal Control Theory for Systems with Distributed Parameters, Nauka, Moscow, 1965 (in Russian).
[001] [2] Yn. V. Egorov, On some optimal control problems, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963), 887-904 (in Russian). | Zbl 0156.31804
[002] [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). | Zbl 0800.65015
[003] [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. | Zbl 0821.49003
[004] [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. | Zbl 0144.34903
[005] [6] A. D. Iskenderov, On a certain inverse problem for quasilinear parabolic equations, Differentsial'nye Uravneniya 10 (1974), 890-898 (in Russian). | Zbl 0285.35040
[006] [7] A. D. Iskenderov and R. K. Tagiev, Optimization problems with controls in coefficients of parabolic equations, ibid. 19 (1983), 1324-1334 (in Russian). | Zbl 0521.49016
[007] [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.
[008] [9] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian).
[009] [10] K. A. Lurie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian).
[010] [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).
[011] [12] A. Mokrane, An existence result via penalty method for some nonlinear parabolic unilateral problems, Boll. Un. Mat. Ital. B 8 (1994), 405-417. | Zbl 0805.35068
[012] [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. | Zbl 0245.49020
[013] [14] E. Polak, Computational Methods in Optimization, Academic Press, New York, 1971.
[014] [15] B. N. Pshenichnyĭ and Yu. M. Danilin, Numerical Methods in Extremal Problems, Mir, Moscow, 1982.
[015] [16] J. B. Rosen, The gradient projection method for nonlinear programming. Part I: Linear constraints, SIAM J. Appl. Math. 8 (1960), 181-217. | Zbl 0099.36405
[016] [17] J. B. Rosen, The gradient projection method for nonlinear programming. Part II: Nonlinear constraints, ibid. 9 (1961), 514-532. | Zbl 0231.90048
[017] [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. | Zbl 0767.49003
[018] [19] F. P. Vasil'ev, Numerical Methods for Solving Extremal Problems, Nauka, Moscow, 1988 (in Russian).