Abstract
A class of mixed controlstate constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentievtype regularized state constrained optimal control is considered. Its numerical solution is obtained via a primaldual activeset method, which is equivalent to a class of semismooth Newton methods. The locally superlinear convergence of the activeset method in function space is established, and its mesh independence is proved. The paper contains a report on numerical test runs including a comparison with a shortstep pathfollowing interiorpoint method and a coarsetofine mesh sweep, that is, a nested iteration technique, for accelerating the overall solution process. Finally, convergence and regularity properties of the regularized problems with respect to a vanishing Lavrentiev parameter are considered.
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