@article{1143.65051,
author="Hinterm\"uller, M. and Tr\"oltzsch, F. and Yousept, I.",
title="{Mesh-independence of semismooth Newton methods for
    Lavrentiev-regularized state constrained nonlinear optimal control
    problems.}",
language="English",
journal="Numer. Math. ",
volume="108",
number="4",
pages="571-603",
year="2008",
doi={10.1007/s00211-007-0134-6},
abstract="{The authors consider the following mixed control-state constrained,
    or equivalently Lavrentiev-regularized state constrained, optimal control
    problem 
 $$\text{minimize }J(u,y):= \tfrac{1}{2}\Vert y- y_d\Vert^2_{L^2}+
    \tfrac{\alpha}{2}\Vert u\Vert^2_{L^2}$$ 
 over $(u,y)\in L^2(\Omega)\times
    H^1_0(\Omega)\cap C(\Omega)$ $$\text{subject to }Ay+ d(\cdot, y)=
    u\quad\text{in }\Omega,$$ 
 where $A$ is a second-order linear elliptic
    differential operator and 
 $$y_a\le \varepsilon u(x)+ y(x)\le
    y_b\quad\text{for almost all }x\in\Omega.$$ Based on the first-order
    necessary optimality conditions for this problem, a semi-smooth Newton
    method is proposed and ist fast local convergence in function space as well
    as a mesh-independence principle for appropriate discretizations are
    proved.\par Numerical tests are presented.}",
reviewer="{Hans Benker (Merseburg)}",
keywords="{numerical examples}",
classmath="{*65K10 (Optimization techniques (numerical methods))
49J20 (Optimal control problems with PDE (existence))
49M15 (Methods of Newton-Raphson, Galerkin and Ritz types)
}",
}