No-gap optimality conditions for an optimal control problem with pointwise control-state constraints |
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| Authors: | Nguyen Hai Son Tran Minh Nguyet |
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| Affiliation: | 1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology , Hanoi, Vietnam.son.nguyenhai1@hust.edu.vn;3. Department of Mathematics, Thang Long University , Hanoi, Vietnam. |
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| Abstract: | An optimal control problem with pointwise mixed constraints of the instationary three-dimensional Navier–Stokes–Voigt equations is considered. We derive second-order optimality conditions and show that there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, the second-order sufficient optimality conditions for the problem where the objective functional does not contain a Tikhonov regularization term are also discussed. |
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| Keywords: | Navier–Stokes–Voigt equations second-order necessary optimality conditions second-order sufficient optimality conditions optimal control no-gap conditions |
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