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Upper semicontinuity of the solution map to a parametric boundary optimal control problem with unbounded constraint sets

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Abstract

The paper studies the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the objective function is nonconvex and the admissible set is unbounded. We show that under certain conditions, the solution set is upper semicontinuous and continuous with respect to parameters.

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Acknowledgements

The authors wish to express their sincere thanks to the anonymous referees for their helpful suggestions and useful comments which improved the original manuscript greatly. The research of the first author is funded by Vietnam Institute for Advanced Study in Mathematics (VIASM). This research of the second author (Tuan Anh Dao) is funded (or partially funded) by the Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology.

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Correspondence to Nguyen Hai Son.

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Son, N.H., Dao, T.A. Upper semicontinuity of the solution map to a parametric boundary optimal control problem with unbounded constraint sets. Optim Lett 16, 1799–1815 (2022). https://doi.org/10.1007/s11590-021-01804-2

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  • DOI: https://doi.org/10.1007/s11590-021-01804-2

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