WIAS Preprint No. 1236, (2007)

Stability of infinite dimensional control problems with pointwise state constraints


  • Hinze, Michael
  • Meyer, Christian

2010 Mathematics Subject Classification

  • 49K20 49N10 49M20


  • Optimal control of semi-linear elliptic equations, pointwise state constraints, finite element approximation




A general class of nonlinear infinite dimensional optimization problems is considered that covers semi-linear elliptic control problems with distributed control as well as boundary control. Moreover, pointwise inequality constraints on the control and the state are incorporated. The general optimization problem is perturbed by a certain class of perturbations, and we establish convergence of local solutions of the perturbed problems to a local solution of the unperturbed optimal control problem. These class of perturbations include finite element discretization as well as data perturbation such that the theory implies convergence of finite element approximation and stability w.r.t. noisy data.

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