On an optimal control problem for a quasilinear parabolic equation

S. Farag; M. Farag

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 2, page 239-250
  • ISSN: 1233-7234

Abstract

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An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.

How to cite

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Farag, S., and Farag, M.. "On an optimal control problem for a quasilinear parabolic equation." Applicationes Mathematicae 27.2 (2000): 239-250. <http://eudml.org/doc/219271>.

@article{Farag2000,
abstract = {An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.},
author = {Farag, S., Farag, M.},
journal = {Applicationes Mathematicae},
keywords = {existence theory; parabolic equations; penalty function methods; optimal control; quasilinear parabolic equation; penalty function technique; existence; uniqueness},
language = {eng},
number = {2},
pages = {239-250},
title = {On an optimal control problem for a quasilinear parabolic equation},
url = {http://eudml.org/doc/219271},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Farag, S.
AU - Farag, M.
TI - On an optimal control problem for a quasilinear parabolic equation
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 2
SP - 239
EP - 250
AB - An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
LA - eng
KW - existence theory; parabolic equations; penalty function methods; optimal control; quasilinear parabolic equation; penalty function technique; existence; uniqueness
UR - http://eudml.org/doc/219271
ER -

References

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  1. [1] M. Bergounioux and F. Tröltzsch, Optimality conditions and generalized bang-bang principle for a state constrained semilinear parabolic problem, Numer. Funct. Anal. Optim. 17 (1996), 517-536. Zbl0858.49021
  2. [2] P. Enidr, Optimal Control and Calculus of Variations, Oxford Sci. Publ., London, 1993. 
  3. [3] M. H. Farag, Application of the exterior penalty method for solving constrained optimal control problem, Math. Phys. Soc. Egypt, 1995. 
  4. [4] M. Goebel, On existence of optimal control, Math. Nachr. 93 (1979), 67-73. Zbl0435.49006
  5. [5] W. Krabs, Optimization and Approximation, Wiley, New York, 1979. 
  6. [6] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Parabolic Equations, Nauka, Moscow, 1976 (in Russian). 
  7. [7] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Nau- ka, Moscow, 1973 (in Russian). Zbl0169.00206
  8. [8] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian). 
  9. [9] K. A. Lourie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian). 
  10. [10] V. P. Mikhailov, Partial Differential Equations, Nauka, Moscow, 1983 (in Russian). 
  11. [11] J. P. Raymond, Nonlinear boundary control semilinear parabolic equations with pointwise state constraints, Discrete Contin. Dynam. Systems 3 (1997), 341-370. Zbl0953.49026
  12. [12] J. P. Raymond and F. Tröltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with constraints, preprint, Fak. Math., Tech. Univ. Chemnitz, 1998. Zbl1010.49015
  13. [13] A. N. Tikhonov and N. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems, Nauka, Moscow, 1974 (in Russian). 
  14. [14] F. Tröltzsch, On the Lagrange-Newton-SQP method for the optimal control for semilinear parabolic equations, preprint, Fak. Math., Tech. Univ. Chemnitz, 1998. Zbl0954.49018
  15. [15] T. 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
  16. [16] A.-Q. Xing, The exact penalty function method in constrained optimal control problems, J. Math. Anal. Appl. 186 (1994), 514-522. Zbl0817.49031

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