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On the Sequential Normal Compactness Condition and its Restrictiveness in Selected Function Spaces

  • Patrick Mehlitz
Article
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Abstract

Sequential normal compactness is one of the most important properties in terms of modern variational analysis. It is necessary for the derivation of calculus rules for the computation of generalized normals to set intersections or preimages of sets under transformations. While sequential normal compactness is inherent in finite-dimensional Banach spaces, its presence has to be checked in the infinite-dimensional situation. In this paper, we show that broad classes of sets in Lebesgue and Sobolev spaces which are reasonable in the context of optimal control suffer from an intrinsic lack of sequential normal compactness.

Keywords

Decomposable set Optimal control Sequential normal compactness 

Mathematics Subject Classification (2010)

28B05 49J53 

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Notes

Acknowledgments

This work is supported by the DFG grant Analysis and Solution Methods for Bilevel Optimal Control Problems within the Priority Program SPP 1962 (Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization).

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Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceTechnische Universität Bergakademie FreibergFreibergGermany

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