@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) }", }