Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations
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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.
KeywordsOptimal control Stationary Navier-stokes equations Solution stability Locally upper Hölder continuity Second-order necessary optimality condition Second-order sufficient optimality condition
Mathematics Subject Classification (2010)49K20 35J25
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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