@article{1131.90073,
author="Hinterm\"uller, M. and Hinze, M.",
title="{A SQP-semismooth Newton-type algorithm applied to control of the
    instationary Navier--Stokes system subject to control constraints.}",
language="English",
journal="SIAM J. Optim. ",
volume="16",
number="4",
pages="1177-1200",
year="2006",
doi={10.1137/030601259},
abstract="{Summary: 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 (QPs) of SQP require a more sophisticated solver when 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 one to argue a quadratic rate of convergence of the SQP-method.
    The paper ends with a report on numerical results supporting the theoretical
    findings.}",
keywords="{box constraints; generalized equations; Navier--Stokes; optimal
    control; semismooth Newton; sequential quadratic programming}",
classmath="{*90C55 (Methods of successive quadratic programming type)
65K10 (Optimization techniques (numerical methods))
49M37 (Methods of nonlinear programming type)
}",
}