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Annular and sectorial sparsity in optimal control of elliptic equations

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Abstract

Optimal control problems are considered with linear elliptic equations in polar coordinates. The objective contains \(L^1\)-type norms, which promote sparse optimal controls. The particular iterated structure of these norms gives rise to either annular or sectorial sparsity patterns. Optimality conditions and numerical solution approaches are developed.

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Acknowledgments

The authors wish to thank two anonymous reviewers for their helpful comments and in particular for the suggestion of an alternative discretization scheme, which led to the addition of Remark 3.2.

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Authors and Affiliations

  1. Faculty of Mathematics, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Roland Herzog, Johannes Obermeier & Gerd Wachsmuth

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  1. Roland Herzog
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  2. Johannes Obermeier
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  3. Gerd Wachsmuth
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Correspondence to Gerd Wachsmuth.

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Herzog, R., Obermeier, J. & Wachsmuth, G. Annular and sectorial sparsity in optimal control of elliptic equations. Comput Optim Appl 62, 157–180 (2015). https://doi.org/10.1007/s10589-014-9721-5

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  • DOI: https://doi.org/10.1007/s10589-014-9721-5

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