MGOPT with gradient projection method for solving bilinear elliptic optimal control problems

Multigrid optimization schemes that solve optimal control problems with bilinear elliptic partial differential equations are presented. For the solution of the control-unconstrained and control-constrained problems, finite difference discretization is utilized. To solve the control-unconstrained case, multigrid for optimization (MGOPT) method is considered and for the control-constrained case, MGOPT with gradient projection method is applied to solve the problem. Numerical experiments show the efficiency of these techniques.