In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the...

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404–424, <CitationRef CitationID="CR23">2002</CitationRef>; J. Eur. Math. Soc. 4:201–236, <CitationRef CitationID="CR24">2002</CitationRef>) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123–3150, <CitationRef CitationID="CR6">2009</CitationRef>), among others....</citationref></citationref></citationref>

In this paper we consider a model elliptic optimal control problem with finitely many state constraints in two and three dimensions. Such problems are challenging due to low regularity of the adjoint variable. For the discretization of the problem we consider continuous linear elements on...