Michael Hintermüller and Michael Hinze
A SQP-Semi-Smooth Newton-type Algorithm applied to Control of the instationary Navier-Stokes System Subject to Control Constraints
Sequential quadratic programming (SQP) methods
for the optimal control of the instationary Navier-Stokes
equations with pointwise constraints on the control are
considered. Due to the presence of the constraints the quadratic
subproblems (QP) of SQP require a more sophisticated solver
compared to the unconstrained case. In this paper, a semismooth
Newton method is proposed for efficiently solving the QPs. The
convergence analysis, which is performed in an appropriate
function space setting, relies on the concept of slant
differentiability for proving locally superlinear convergence of
the QP-solver. For the analysis of the outer SQP-iteration a
generalized equations approach is utilized. Sufficient conditions
for guaranteeing strong regularity of the generalized equation are
established which, in turn, allows to argue a quadratic rate of
convergence of the SQP-method. The paper ends with a report on
numerical results supporting the theoretical findings.
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