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\(L^\infty \)-Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations

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Abstract

This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the strictly nonnegative second-order optimality conditions, then the solution map is upper Hölder continuous in \(L^\infty \)-norm of control variable.

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Acknowledgements

The research of the first author and the second author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2019.308. This work was also supported by the Ministry of Science and Technology, Taiwan (grant No. MOST 108-2115-M-037-001). The authors would like to thank the anonymous referees for their comments and suggestions which improve the paper 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

    Bui Trong Kien

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

    Nguyen Quoc Tuan

  3. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan, ROC

    Ching-Feng Wen

  4. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan, ROC

    Ching-Feng Wen

  5. Center for General Education, China Medical University, Taichung, 40402, Taiwan, ROC

    Jen-Chih Yao

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  1. Bui Trong Kien
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  2. Nguyen Quoc Tuan
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  3. Ching-Feng Wen
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  4. Jen-Chih Yao
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Correspondence to Ching-Feng Wen.

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Kien, B.T., Tuan, N.Q., Wen, CF. et al. \(L^\infty \)-Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations. Appl Math Optim 84, 849–876 (2021). https://doi.org/10.1007/s00245-020-09664-5

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