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.
@article{bwmeta1.element.bwnjournal-article-zmv27i2p239bwm, author = {S. Farag and M. Farag}, title = {On an optimal control problem for a quasilinear parabolic equation}, journal = {Applicationes Mathematicae}, volume = {27}, year = {2000}, pages = {239-250}, zbl = {0996.49001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i2p239bwm} }
Farag, S.; Farag, M. On an optimal control problem for a quasilinear parabolic equation. Applicationes Mathematicae, Tome 27 (2000) pp. 239-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i2p239bwm/
[000] [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. | Zbl 0858.49021
[001] [2] P. Enidr, Optimal Control and Calculus of Variations, Oxford Sci. Publ., London, 1993.
[002] [3] M. H. Farag, Application of the exterior penalty method for solving constrained optimal control problem, Math. Phys. Soc. Egypt, 1995.
[003] [4] M. Goebel, On existence of optimal control, Math. Nachr. 93 (1979), 67-73. | Zbl 0435.49006
[004] [5] W. Krabs, Optimization and Approximation, Wiley, New York, 1979.
[005] [6] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Parabolic Equations, Nauka, Moscow, 1976 (in Russian).
[006] [7] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Nau- ka, Moscow, 1973 (in Russian). | Zbl 0169.00206
[007] [8] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian).
[008] [9] K. A. Lourie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian).
[009] [10] V. P. Mikhailov, Partial Differential Equations, Nauka, Moscow, 1983 (in Russian).
[010] [11] J. P. Raymond, Nonlinear boundary control semilinear parabolic equations with pointwise state constraints, Discrete Contin. Dynam. Systems 3 (1997), 341-370. | Zbl 0953.49026
[011] [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. | Zbl 1010.49015
[012] [13] A. N. Tikhonov and N. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems, Nauka, Moscow, 1974 (in Russian).
[013] [14] F. Tröltzsch, On the Lagrange-Newton-SQP method for the optimal control for semilinear parabolic equations, preprint, Fak. Math., Tech. Univ. Chemnitz, 1998. | Zbl 0954.49018
[014] [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. | Zbl 0767.49003
[015] [16] A.-Q. Xing, The exact penalty function method in constrained optimal control problems, J. Math. Anal. Appl. 186 (1994), 514-522. | Zbl 0817.49031