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In this paper we apply an augmented Lagrange method to a class of semilinearelliptic optimal control problems with pointwise state constraints. We showstrong convergence of subsequences of the primal variables to a local solutionof the original problem as well as weak convergence of the adjoint states andweak* convergence of the multipliers associated to the state constraint.Moreover, we show existence of stationary points in arbitrary smallneighborhoods of local solutions of the original problem. Additionally, variousnumerical results are presented.

A Lagrange Multiplier Method for Semilinear Elliptic State Constrained Optimal Control Problems