A semismooth newton multigrid method for constrained elliptic optimal control problems

Abstract

A multigrid scheme is proposed for solving the Schur complement linear systems arising in each Newton iteration when the semi-smooth Newton method is applied to solve control-constrained elliptic optimal control problems. Numerical experiments are performed to illustrate the high efficiency of our proposed method. Computation simulation shows that the convergence rate is quite robust as the regularization parameter approaches to zero.