Computational Optimization and Applications

, Volume 62, Issue 1, pp 157–180 | Cite as

Annular and sectorial sparsity in optimal control of elliptic equations

  • Roland Herzog
  • Johannes Obermeier
  • Gerd Wachsmuth


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.


Directional sparsity Polar coordinates Coordinate transformation 

Mathematics Subject Classification

49K20 65K10 49M15 



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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Roland Herzog
    • 1
  • Johannes Obermeier
    • 1
  • Gerd Wachsmuth
    • 1
  1. 1.Faculty of MathematicsTechnische Universität ChemnitzChemnitzGermany

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