In this paper, a class of parametric optimal control problems governed by stationary Navier-Stokes equations with mixed pointwise constraints is considered. We give no-gap second-order necessary and sufficient conditions for unperturbed problem. We show that if the strictly second-order sufficient condition for unperturbed problem is valid and the objective function is locally Lipschitz continuous, then the solution map is locally upper Hölder continuous at the reference parameter.
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This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2015.13.
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Kien, B.T. Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations. Acta Math Vietnam 44, 431–448 (2019). https://doi.org/10.1007/s40306-018-00304-3
- Optimal control
- Stationary Navier-stokes equations
- Solution stability
- Locally upper Hölder continuity
- Second-order necessary optimality condition
- Second-order sufficient optimality condition