Article

Computational Optimization and Applications

, Volume 42, Issue 1, pp 43-66

First online:

A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints

  • F. TröltzschAffiliated withInstitut für Mathematik, Technische Universität Berlin Email author 
  • , I. YouseptAffiliated withInstitut für Mathematik, Technische Universität Berlin

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Abstract

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.

Keywords

Boundary control State constraints Lavrentiev type regularization Semismooth Newton method Optimize-then-discretize Nested iteration