A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints
- 163 Downloads
A Lavrentiev type regularization technique for solving elliptic boundary control problems with pointwise state constraints is considered. The main concept behind this regularization is to look for controls in the range of the adjoint control-to-state mapping. After investigating the analysis of the method, a semismooth Newton method based on the optimality conditions is presented. The theoretical results are confirmed by numerical tests. Moreover, they are validated by comparing the regularization technique with standard numerical codes based on the discretize-then-optimize concept.
KeywordsBoundary control State constraints Lavrentiev type regularization Semismooth Newton method Optimize-then-discretize Nested iteration
Unable to display preview. Download preview PDF.
- 7.Hackbusch, W.: Multigrid Methods and Applications. Springer Series in Computational Mathematics, vol. 4. Springer, Berlin (1985) Google Scholar
- 9.Hintermüller, M., Tröltzsch, F., Yousept, I.: Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems (2006) Google Scholar
- 15.Meyer, C., Tröltzsch, F.: On an elliptic optimal control problem with pointwise mixed control-state constraints. In: Seeger, A. (ed.) Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization held in Avignon, September 20–24, 2004. Lectures Notes in Economics and Mathematical Systems, vol. 563, pp. 187–204. Springer, Berlin (2006) CrossRefGoogle Scholar