Stability of semilinear elliptic optimal control problems with pointwise state constraints

Authors:
M. Hinze;C. Meyer
Affiliations:
Mathematical Department, University Hamburg, Hamburg, Germany 20146;Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany 64293
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

A semi-linear elliptic control problems with distributed control and pointwise inequality constraints on the control and the state is considered. 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. This 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.