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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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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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