Penalty method for the state equation for an elliptical optimal control problem
We solve an optimal control problem of a system governed by a linear elliptic equation with pointwise control constraints and non-local state constraints by finite difference method. A discrete optimal control problem is approximated by a minimization problem with penaltized state equation. We derive an error estimates. We also prove the rate of convergence of block Gauss-Zeidel iterative solution method for the penaltized problem. We present the results of the numerical experiments.