Multigrid Approaches for Optimization Problems

We focus our discussion on gradient based methods for constrained optimization problems. The expensive part in such methods is the equation solver per each optimization step (and in addition to this the solver for the adjoint equation in the adjoint method). Although these equations may be solved only approximately, still they consist the major part of the solution time.

Multigrid methods can be used in a variety of ways to accelerate gradient based optimizers. We distinguish between multigrid methods that are used for the acceleration of a step in some optimization procedure to genuinely multigrid methods that aim at the full optimization problem.