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Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints

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  • In this paper we report conditions ensuring Lipschitz continuity of optimal control and Lagrange multipliers for a dynamic optimization problem with inequality pure state and mixed state-control constraints.
    Mathematics Subject Classification: Primary: 49K15, 49K40.

    Citation:

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  • [1]

    J. F. Bonnans and A. Hermant, Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints, Ann. I. H. Poincaré - Analyse Non Linéaire, 26 (2009), 561-598.

    [2]

    J. F. Bonnans and A. Shapiro, "Perturbation Analysis of Optimization Problems," Springer-Verlag, New York, 2000.

    [3]

    A. V. Dmitruk, Maximum principle for a general optimal control problem with state and regular mixed constraints, Comp. Math. and Modeling, 4 (1993), 364-377.doi: doi:10.1007/BF01128760.

    [4]

    G. N. Galbraith and R. B. Vinter, Lipschitz Continuiuty of Optimal Controls for State Constrained Problems, SIAM J. Control and Optimization, 42 (2003), 1727-1744.doi: doi:10.1137/S0363012902404711.

    [5]

    W. W. Hager, Lipschitz continuity for constrained processes, SIAM J. Control and Optimization, 17 (1979), 321-338.doi: doi:10.1137/0317026.

    [6]

    K. Malanowski, On the regularity of solutions to optimal control problems for systems linear with respect to control variable, Arch. Auto. i Telemech., 23 (1978), 227-241.

    [7]

    K. Malanowski, On normality of Lagrange multipliers for state constrained optimal control problems, Optimization, 52 (2003), 75-91.doi: doi:10.1080/0233193021000058940.

    [8]

    A. A. Milyutin, A. V. Dmitruk and N. P. Osmolovsky, "Maximum Principle in Optimal Control" (Russian), Moscow State University Press, 2004. Available online at http://www.milyutin.ru/book.html.

    [9]

    S. M. Robinson and R. H. Day, A sufficient condition for continuity of optimal sets in mathematical programming, J. Math. Anal. Appl., 45 (1974), 506-511.doi: doi:10.1016/0022-247X(74)90089-4.

    [10]

    S. M. Robinson, Strongly regular generalized equations, Mathematics of Operations Research, 5 (1980), 43-62.doi: doi:10.1287/moor.5.1.43.

    [11]

    I. Shvartsman and R. B. Vinter, Regularity properties of optimal controls for state constrained problems with time-varying control constraints, Nonlinear Analysis: Theory, Methods and Applications, 65 (2006), 448-474.

    [12]

    R. B. Vinter, "Optimal Control," Birkhäuser, Boston, 2000.

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