Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
Idczak, Dariusz ; Majewski, Marek ; Walczak, Stanisław
International Journal of Applied Mathematics and Computer Science, Tome 13 (2003), p. 29-44 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:207621
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     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},
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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