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A general statement of dual first-order sufficient optimality conditions for the generalized problem of Bolza

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EN
Abstrakty
EN
In this paper we provide first-order sufficient optimality conditions for the generalized problem of Bolza when all arcs take values in a separable Hilbert space. Our approach consists in the explicit construction of a quadratic function that satisfies the dual Hamilton-Jacobi inequality. The essential role in the generalized conditions plays the existence of a certain function for which a certain inequality holds.
Wydawca
Rocznik
Strony
711--720
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Faculty of Mathematics, University of Łódź, ul. Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] V. Barbu and Th. Precupanu, Convexity and Optimization in Banach Spaces, D. Reidel Publishing Company, Dordrecht, 1986.
  • [2] F. H. Clarke, Generalized gradients and applications, Trans. Amer. Soc. 205 (1975), 247-262.
  • [3] F. H. Clarke, The generalized problem of Bolza, SIAM J. Control Optim. 14 (1976), 682-699.
  • [4] F. H. Clarke, Generalized gradients of Lipschitz functionals, Advances in Math. 40 (1981), 52-67.
  • [5] F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983.
  • [6] F. H. Clarke, Hamiltonian analysis of the generalized problem of Bolza, Trans. Amer. Soc. 301 (1987), 385-400.
  • [7] F. H. Clarke and V. Zeidan, Sufficiency and the Jacobi conditions in the calculus of variations, Canadian J. Math. 38 (1986), 1199-1209.
  • [8] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.
  • [9] H. Gajewski, K. Groege r and K. Zacharias, Nichtlineare operatorgleichungen und operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.
  • [10] M. R. Hestenes, Calculus of Variations and Optimal Control Theory, John Wiley & Sons, New York, 1966.
  • [11] E. Młynarska, Dual sufficient optimality conditions for the generalized problem of Bolza, J. Optim. Theory Appl. 104, No. 2 (2000), 427-442.
  • [12] Nowakowski, The Dual Dynamic Programming, Proc. Amer. Math. Soc. 116, No. 4 (1992), 1089-1096.
  • [13] R. T. Rockafellar, Conjugate convex functions in the optimal control and the calculus of variations, J. Math. Anal. Appl. 32 (1970), 174-222.
  • [14] R. T. Rockafellar, Generalized Hamiltonian equations for convex problems of Lagrange, Pacific J. Math. 33 (1970), 411-427.
  • [15] R. T. Rockafellar, Opimal arcs and the minimum value function in problems of Lagrange, Trans. Amer. Math. Soc. 180 (1973), 53-83.
  • [16] V. Zeidan, Sufficient conditions for the generalized problem of Bolza, Trans. Amer. Math. Soc. 275 (1983), 561-586.
  • [17] V. Zeidan, First and second-order sufficient conditions for opimal control and the calculus of variations, Appl. Math. Optim. 11 (1984), 209-226.
  • [18] V. Zeidan, A modified Hamilton-Jacobi approach in the generalized problem of Bolza, Appl. Math. Optim. 11 (1984), 97-109.
  • [19] K. Yosida, Functional Analysis, Springer Verlag, New York. 1974.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0007-0023
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