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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

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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.

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Acknowledgments

The authors wish to express their sincere thanks to the anonymous referees for their helpful suggestions and comments which improved the original manuscript greatly. The first author would like to thank the Alexander von Humboldt Foundation and the University of Duisburg-Essen for financial support and hospitality.

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Authors and Affiliations

  1. Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi, Vietnam

    B. T. Kien

  2. Faculty of Information Technology, National Institute of Education Management, 31 Phan Dinh Giot, Hanoi, Vietnam

    V. H. Nhu

  3. Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Straße 9, 45127 , Essen, Germany

    A. Rösch

Authors
  1. B. T. Kien
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  2. V. H. Nhu
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  3. A. Rösch
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Correspondence to A. Rösch.

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Communicated by B. Dacorogna.

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Kien, B.T., Nhu, V.H. & Rösch, A. Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints. J Optim Theory Appl 165, 30–61 (2015). https://doi.org/10.1007/s10957-014-0628-1

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  • DOI: https://doi.org/10.1007/s10957-014-0628-1

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