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Abstrakty
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.
Rocznik
Tom
Strony
29--44
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90–238 Łódź, Poland
autor
- University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90–238 Łódź, Poland
autor
- University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90–238 Łódź, Poland
Bibliografia
- [1] Aubin J.P. and Frankowska H. (1990): Set-Valued Analysis. — Boston: Birkhäuser.
- [2] Bank B., Guddat J., Klatte D., Kummer B. and Tammer K. (1983): Non-Linear Parametric Optimization. — Basel: Birkhäuser.
- [3] Bergmann J., Burgemeier P. and Weiher P. (1989): Explicit controllability criteria for Goursat problem. — Optim., Vol. 20, No. 3, pp. 281–290.
- [4] Ekeland I. and Temam R. (1976): Convex Analysis and Variational Problems. — Amsterdam: North-Holland Publishing Company.
- [5] Fiacco A.V. (1981): Sensitivity analysis for nonlinear programming using penalty methods.—Math. Programm., Vol. 10, No. 3, pp. 287–311.
- [6] Idczak D. (1990): Optimization of systems described by partial differential equations. — Ph. D. Thesis, University of Łódź, Poland, (in Polish).
- [7] Idczak D. (1996): The generalization of the Du Bois-Reymond lemma 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.
- [8] Idczak D. (1998): Optimal control of a coercive Dirichlet Problem. — SIAM J. Contr. Optim., Vol. 36, No. 4, pp. 1250–1276.
- [9] Idczak D. and Rogowski A., (2003): On a generalization of Krasnoselskii’s theorem. — J. Austral. Math. Soc., Ser. A, (to appear).
- [10] 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.
- [11] Idczak D., Kibalczyc K. and Walczak S. (1994): On an optimization problem with cost of rapid variation of control. — J. Austral. Math. Soc., Ser. B, Vol. 86, No.1, pp. 117–131.
- [12] 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.
- [13] Kisielewicz M., (1991): Differential Inclusions and Optimal Control. — Dordrecht-Warsaw: Kluwer Academic Publishers–Polish Scientific Publishers.
- [14] 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.
- [15] Łojasiewicz S. (1988): An Introduction to the Theory of Real Functions. — Chichester: Wiley.
- [16] 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.
- [17] Pulvirenti G. and Santagati G. (1975): Sulla controllabilita completa in Luogo determinato ed in luogo variabile por un processo di controllo con parametri dostributi. — Boll. UMI, Vol. 11, No. 3, pp. 316–328, (in Italian).
- [18] Robinson S.M. (1974): Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear systems. — Math. Programm., 7, pp. 1–16.
- [19] 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.
- [20] Robinson S.M. (1980): Strongly regular generalized equations. —Math. Oper. Res., Vol. 5, No. 1, pp. 43–62.
- [21] Surryanarayama M.B. (1973): Necessary conditions for optimization problems with hyperbolic partial differential equations.—SIAM J. Contr., Vol. 11, No. 4, pp. 130–147.
- [22] Tikhonov A.N. and Samarski A.A. (1958): Equations of Mathematical Physics.—Moscow: GITTL, (in Russian).
- [23] 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.
- [24] Walczak S. (2001): Well-posed and ill-posed optimal control problems.—JOTA, Vol. 109, No. 1, pp. 169–185.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPZ1-0002-0003