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Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints

Author

Listed:
  • B. T. Kien

    (Institute of Mathematics, Vietnam Academy of Science and Technology)

  • V. H. Nhu

    (National Institute of Education Management)

  • A. Rösch

    (University of Duisburg-Essen)

Abstract

Based on some tools of variation analysis, we deal with first- and second-order necessary optimality conditions for a class of optimal control problems governed by semilinear elliptic equations and stationary Navier–Stokes equations with pure state constraints. To do this, we first derive optimality conditions for an abstract optimal control problem and then apply the obtained results to derive second-order necessary optimality conditions for semilinear elliptic optimal control problems as well as optimal control problems governed by stationary Navier–Stokes equations.

Suggested Citation

  • B. T. Kien & V. H. Nhu & A. Rösch, 2015. "Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 30-61, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0628-1
    DOI: 10.1007/s10957-014-0628-1
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    References listed on IDEAS

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    1. J. P. Raymond & H. Zidani, 1999. "Pontryagin's Principle for Time-Optimal Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 375-402, May.
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