# The gradient projection method for solving an optimal control problem

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 2, page 141-147
- ISSN: 1233-7234

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topFarag, M.. "The gradient projection method for solving an optimal control problem." Applicationes Mathematicae 24.2 (1997): 141-147. <http://eudml.org/doc/219158>.

@article{Farag1997,

abstract = {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.},

author = {Farag, M.},

journal = {Applicationes Mathematicae},

keywords = {distributed parameter systems; boundary value problems; gradient methods; optimal control; optimal control problem; parabolic equation; gradient projection method; distributed parameter system},

language = {eng},

number = {2},

pages = {141-147},

title = {The gradient projection method for solving an optimal control problem},

url = {http://eudml.org/doc/219158},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Farag, M.

TI - The gradient projection method for solving an optimal control problem

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 2

SP - 141

EP - 147

AB - 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.

LA - eng

KW - distributed parameter systems; boundary value problems; gradient methods; optimal control; optimal control problem; parabolic equation; gradient projection method; distributed parameter system

UR - http://eudml.org/doc/219158

ER -

## References

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- [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). Zbl0800.65015
- [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. Zbl0821.49003
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- [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. Zbl0805.35068
- [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. Zbl0245.49020
- [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. Zbl0099.36405
- [17] J. B. Rosen, The gradient projection method for nonlinear programming. Part II: Nonlinear constraints, ibid. 9 (1961), 514-532. Zbl0231.90048
- [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. Zbl0767.49003
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