Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints

An elliptic optimal control problem with constraints on the state variable isconsidered. The Lavrentiev-type regularization is used to treat the constraintson the state variable. To solve the problem numerically, the multigrid foroptimization (MGOPT) technique and the collective smoothing multigrid (CSMG)are implemented. Numerical results are reported toillustrate and compare the efficiency of both multigrid strategies.