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Second-order optimality conditions and regularity of Lagrange multipliers for mixed optimal control problems

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This paper deals with second-order optimality conditions and regularity of Lagrange multipliers for a class of optimal control problems governed by semilinear elliptic equations with mixed pointwise constraints in which controls act both in the domain and on the boundary. We give some criteria under which the optimality conditions are of KKT type and the multipliers are of \(L^p\)-spaces. Moreover, we show that the multipliers are Lipschitz continuous functions.

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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.

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Authors and Affiliations

  1. Faculty of Information Technology, National University of Civil Engineering, 55 Giai Phong Str., Hanoi, Vietnam

    N. B. Giang

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

    N. Q. Tuan

  3. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

    N. H. Son

Authors
  1. N. B. Giang
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  2. N. Q. Tuan
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  3. N. H. Son
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Correspondence to N. H. Son.

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The research is funded by National University of Civil Engineering (NUCE) under grant number 205 - 2018/KHXD-TD.

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Giang, N.B., Tuan, N.Q. & Son, N.H. Second-order optimality conditions and regularity of Lagrange multipliers for mixed optimal control problems. Positivity 25, 911–937 (2021). https://doi.org/10.1007/s11117-020-00793-3

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