In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.
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