Multigrid optimization methods for linear and bilinear elliptic optimal control problems (Q956683)

The authors consider elliptic linear and bilinear optimal control problems of the following form \[ \min_{u\in U}\,J(y, u),\quad c(y,u)= 0, \] where \(c(y,u)= 0\) is an elliptic partial differential equation with given boundary conditions. For the solution of these problems, the multigrid for optimization method and the collective smoothing multigrid method are developed and compared. -- Numerical experiments are presented.