In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
@article{bwmeta1.element.bwnjournal-article-amcv13i1p29bwm, author = {Idczak, Dariusz and Majewski, Marek and Walczak, Stanis\l aw}, title = {Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {13}, year = {2003}, pages = {29-44}, zbl = {1052.93053}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p29bwm} }
Idczak, Dariusz; Majewski, Marek; Walczak, Stanisław. Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 29-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i1p29bwm/
[000] Aubin J.P. and Frankowska H. (1990): Set-Valued Analysis. - Boston: Birkhauser. | Zbl 0713.49021
[001] Bank B., Guddat J., Klatte D., Kummer B. and Tammer K.(1983): Non-Linear Parametric Optimization. - Basel: Birkhauser. | Zbl 0502.49002
[002] Bergmann J., Burgemeier P. and Weiher P. (1989): Explicit controllability criteria for Goursat problem. - Optim., Vol. 20, No. 3, pp. 281-290. | Zbl 0673.93004
[003] Ekeland I. and Temam R. (1976): Convex Analysis and Variational Problems. - Amsterdam: North-Holland Publishing Company. | Zbl 0322.90046
[004] Fiacco A.V. (1981): Sensitivity analysis for nonlinear programming using penalty methods. - Math. Programm., Vol. 10, No. 3, pp. 287-311. | Zbl 0357.90064
[005] Idczak D. (1990): Optimization of systems described by partial differential equations. - Ph. D. Thesis, University of Lódź, Poland, (in Polish).
[006] Idczak D. (1996): The generalization of the Du Bois-Reymondlemma for functions of two variables to the case of partial derivatives of any order. - Topology in Nonlinear Analysis, Banach Center Publications, Vol. 35, pp. 221-236. | Zbl 0868.49015
[007] Idczak D. (1998): Optimal control of a coercive Dirichlet Problem. - SIAM J. Contr. Optim., Vol. 36, No. 4, pp. 1250-1276. | Zbl 0916.49017
[008] Idczak D. and Rogowski A., (2003): On a generalization of Krasnoselskii's theorem. - J. Austral.Math. Soc., Ser. A, (to appear). | Zbl 1030.47044
[009] Idczak D. and Walczak S. (1994): On Helly's theorem for functions of several variables and its applications to variational problems, Optim., Vol. 30, No. 4, pp. 331-343. | Zbl 0817.49007
[010] Idczak D., Kibalczyc K. and Walczak S. (1994): On anoptimization problem with cost of rapid variation of control. - J. Austral. Math. Soc., Ser. B, Vol. 86, No.1, pp. 117-131. | Zbl 0837.49005
[011] Ioffe A. (1994): On sensitivity analysis of nonlinear programs in Banach spaces: the approach via composite unconstrained optimization. - SIAM J. Optim., Vol. 4, No. 1, pp. 1-43. | Zbl 0820.90105
[012] Kisielewicz M., (1991): Differential Inclusions and Optimal Control. - Dordrecht-Warsaw: Kluwer Academic Publishers-Polish Scientific Publishers. | Zbl 0731.49001
[013] Levitin E.S. (1975): On the local perturbation theory of a problem of mathematical programming in a Banach space. - Soviet Math. Dokl., Vol. 16, No. 5, pp. 1354-1358. | Zbl 0337.90058
[014] Łojasiewicz S. (1988): An Introduction to the Theory of Real Functions. - Chichester: Wiley. | Zbl 0653.26001
[015] Malanowski K. (1993): Stability and sensitivity analysis of solutions to infinite-dimensional optimization problems. - Proc.16-th IFIP Conf. System Modelling and Optimization, Compiegne, France, pp. 109-127. | Zbl 0810.90137
[016] Pulvirenti G. and Santagati G. (1975): Sulla controllabilita completa in Luogo determinato ed in luogo variabile por un processo dicontrollo con parametri dostributi. - Boll. UMI, Vol. 11, No. 3, pp. 316-328, (in Italian). | Zbl 0319.93013
[017] Robinson S.M. (1974): Perturbed Kuhn-Tucker points andrates of convergence for a class of nonlinear systems. - Math.Programm., 7, pp. 1-16. | Zbl 0294.90078
[018] Robinson S.M. (1976): Stability theory for system of inequalities, Part II: Differentiable nonlinear systems. - SIAM J. Numer. Anal. Vol. 13, No. 4, pp. 497-513. | Zbl 0347.90050
[019] Robinson S.M. (1980): Strongly regular generalized equations. - Math. Oper. Res., Vol. 5, No. 1, pp. 43-62. | Zbl 0437.90094
[020] Surryanarayama M.B. (1973): Necessary conditions for optimization problems with hyperbolic partial differential equations. - SIAM J. Contr., Vol. 11, No. 4, pp. 130-147.
[021] Tikhonov A.N. and Samarski A.A. (1958): Equations of Mathematical Physics. - Moscow: GITTL, (in Russian).
[022] Walczak S. (1987): Absolutely continuous functions of several variables and their applications to differential equations. - Bull. Pol. Acad. Sci., Ser. Math., Vol. 35, No. 11-12, pp. 733-744. | Zbl 0691.35029
[023] Walczak S. (2001): Well-posed and ill-posed optimal control problems. - JOTA, Vol. 109, No. 1, pp. 169-185. | Zbl 0991.49019