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2003 | 13 | 1 | 29-44

Tytuł artykułu

Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
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

13

Numer

1

Strony

29-44

Opis fizyczny

Daty

wydano
2003
otrzymano
2002-09-01
poprawiono
2003-01-01

Twórcy

  • University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90-238 Łódź, Poland
  • University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90-238 Łódź, Poland
  • University of Łódź, Faculty of Mathematics, ul. S. Banacha 22, 90-238 Łódź, Poland

Bibliografia

  • Aubin J.P. and Frankowska H. (1990): Set-Valued Analysis. - Boston: Birkhauser.
  • Bank B., Guddat J., Klatte D., Kummer B. and Tammer K.(1983): Non-Linear Parametric Optimization. - Basel: Birkhauser.
  • Bergmann J., Burgemeier P. and Weiher P. (1989): Explicit controllability criteria for Goursat problem. - Optim., Vol. 20, No. 3, pp. 281-290.
  • Ekeland I. and Temam R. (1976): Convex Analysis and Variational Problems. - Amsterdam: North-Holland Publishing Company.
  • Fiacco A.V. (1981): Sensitivity analysis for nonlinear programming using penalty methods. - Math. Programm., Vol. 10, No. 3, pp. 287-311.
  • Idczak D. (1990): Optimization of systems described by partial differential equations. - Ph. D. Thesis, University of Lódź, Poland, (in Polish).
  • 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.
  • Idczak D. (1998): Optimal control of a coercive Dirichlet Problem. - SIAM J. Contr. Optim., Vol. 36, No. 4, pp. 1250-1276.
  • Idczak D. and Rogowski A., (2003): On a generalization of Krasnoselskii's theorem. - J. Austral.Math. Soc., Ser. A, (to appear).
  • 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.
  • 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.
  • 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.
  • Kisielewicz M., (1991): Differential Inclusions and Optimal Control. - Dordrecht-Warsaw: Kluwer Academic Publishers-Polish Scientific Publishers.
  • 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.
  • Łojasiewicz S. (1988): An Introduction to the Theory of Real Functions. - Chichester: Wiley.
  • 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.
  • 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).
  • Robinson S.M. (1974): Perturbed Kuhn-Tucker points andrates of convergence for a class of nonlinear systems. - Math.Programm., 7, pp. 1-16.
  • 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.
  • Robinson S.M. (1980): Strongly regular generalized equations. - Math. Oper. Res., Vol. 5, No. 1, pp. 43-62.
  • Surryanarayama M.B. (1973): Necessary conditions for optimization problems with hyperbolic partial differential equations. - SIAM J. Contr., Vol. 11, No. 4, pp. 130-147.
  • Tikhonov A.N. and Samarski A.A. (1958): Equations of Mathematical Physics. - Moscow: GITTL, (in Russian).
  • 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.
  • Walczak S. (2001): Well-posed and ill-posed optimal control problems. - JOTA, Vol. 109, No. 1, pp. 169-185.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

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