@article{1154.65057,
author="Hinterm\"uller, M.",
title="{Mesh independence and fast local convergence of a primal-dual active-set
    method for mixed control-state constrained elliptic control problems.}",
language="English",
journal="ANZIAM J. ",
volume="49",
number="1",
pages="1-38",
year="2007",
abstract="{An optimal control problem with pure state constraints and a
    second-order linear elliptic differential equation is considered. The
    Lagrange multiplier associated with the pointwise almost everywhere state
    constraints is a Borel measure. Consequently, numerical methods are
    difficult to realize. A Lavrentiev-type regularization of pointwise state
    constrains is proposed. An alternative path follows a generalized
    Moreau-Yosida-type regularization. This gives a mixed control-state
    constrained control problem. The regulized problem is solved efficiently by
    a semismooth Newton method. The method is mesh independent and it is
    superlinear convergent. The paper contains a report on numerical test runs
    including a comparison with a short-step path-following interior-point
    method and a coarse-to-fine mesh sweep. Certain convergence and smoothness
    properties of the solution are proved, even if the Lavrentiev parameter
    vanishes.}",
reviewer="{Werner H. Schmidt (Greifswald)}",
keywords="{PDE-constraints; primal-dual-method; active-set strategy;
    mesh-indepence; mixed control-state constraints; semi-smooth Newton method;
    numerical examples; superlinear convergence; optimal control; second-order
    linear elliptic differential equation; Lagrange multiplier; Lavrentiev-type
    regularization; Moreau-Yosida-type regularization; path-following
    interior-point method}",
classmath="{*65K10 (Optimization techniques (numerical methods))
49J20 (Optimal control problems with PDE (existence))
49M37 (Methods of nonlinear programming type)
}",
}