A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD (Q2839164)

The paper deals with a class of optimal control problems for semilinear parabolic equations. If \(\widetilde{u}\) is a numerical approximation for a locally optimal control, the authors propose to quantify the error \(\|\widetilde{u}-\overline{u}\|\) in an appropriate norm, where \(\overline{u}\) is the nearest locally optimal control. They apply a perturbation method to suboptimal controls \(\widetilde{u}\) obtained by POD (proper orthogonal decomposition). The function \(\overline{u}\) is supposed to satisfy a standard second-order sufficient optimality condition. The associated coercivity constant of the reduced Hessian operator is estimated numerically.NEWLINENEWLINETwo optimal control problems are studied to illustrate the ideas: a distributed optimal control problem for a semilinear parabolic state equation and a boundary control problem for a parabolic state equation.