On the Multiscale Solution of Constrained Minimization Problems

For the constrained minimization of convex or non-convex functionals on the basis of multilevel or domain decomposition methods, different strategies have been proposed within the last decades. These include nonlinear and monotone multigrid methods, see [5, 9, 12, 16, 20], multilevel optimization strategies and multilevel Trust-Region methods, see [8, 21], nonlinear domain decomposition methods [1, 6, 22, 23], multigrid methods as linear solvers in the framework of interior point based methods, see [4, 24] and multigrid methods applied in the framework of primal-dual active set strategies or semi-smooth Newton methods, see [11] for the latter. For a nonlinear multigrid method for smooth problems we refer to [10]. We remark that the references given here are far from exhaustive and refer the reader to the references cited therein.