“…In [5,21,38,51], the authors used preconditioned Krylov subspace methods to solve the first order optimality system by constructing some block preconditioners. In [6,7,8,37,40,46], the authors used mutigrid methods to design fast solvers. Another strategy is to use domain decomposition methods to deal with optimal control problems (see e.g., [2,3,4,12,11,17,25,24,34,43,42]).…”