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Locally Lipschitz Stability of a Parametric Semilinear Elliptic Optimal Control Problem with Mixed Constraints

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Abstract

This paper is concerned with the stability of minimizers to a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise control-state constraints. Under the strictly nonnegative second-order optimality condition assumption, we show that the solution map is locally Lipschitz continuous in \(L^2-\)norm as well as in \(L^\infty -\)norm of the control variable.

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Acknowledgements

This research was supported by International Centre for Research and Postgraduate Training in mathematics, Institute of Mathematics, VAST, under grant number ICRTM01\(-\)2021.01. The author wishes to express his sincere thanks to the anonymous referees for their helpful suggestions and useful comments which improved the original manuscript greatly.

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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

    Quoc Tuan Nguyen

  2. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Quoc Tuan Nguyen

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  1. Quoc Tuan Nguyen
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Correspondence to Quoc Tuan Nguyen.

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Communicated by Boris Vexler.

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Nguyen, Q.T. Locally Lipschitz Stability of a Parametric Semilinear Elliptic Optimal Control Problem with Mixed Constraints. J Optim Theory Appl 197, 939–965 (2023). https://doi.org/10.1007/s10957-023-02226-z

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  • DOI: https://doi.org/10.1007/s10957-023-02226-z

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