We study barrier methods for state constrained optimal control problems with PDEs. In the focus of our analysis is the path of minimizers of the bar-rier subproblems with the aim to provide a solid theoretical basis for function space oriented path-following algorithms. We establish results on existence, continuity, and convergence of this path. Moreover, we consider the structure of barrier subdierentials, which play the role of dual variables.
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Anton Schiela (2009) studied this question.
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