A SQP-Semismooth Newton-type Algorithm applied to Control of the instationary Navier--Stokes System Subject to Control Constraints

M. Hintermüller, M. Hinze
2006 SIAM Journal on Optimization  
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,
more » ... es 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.
doi:10.1137/030601259 fatcat:tktjgoeuxbexzgjnfosmjlg3mi