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Optimal Control of Coupled Systems of Partial Differential Equations pp 139–153Cite as

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Lavrentiev Prox-regularization Methods for Optimal Control Problems with Pointwise State Constraints

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Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 158))

Abstract

A Lavrentiev prox-regularization method for optimal control problems with pointwise state constraints is introduced. The convergence of the controls generated by the iterative Lavrentiev prox-regularization algorithm is studied. For a sequence of regularization parameters that converges to zero, strong convergence of the generated control sequence to the optimal control is proved. Due to the prox-character of the proposed regularization, the feasibility of the iterates for a given parameter can be improved compared with the non-prox Lavrentiev regularization.

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References

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Author information

Authors and Affiliations

  1. Lehrstuhl 2 für Angewandte Mathematik, Martensstr. 3, D-91058, Erlangen, Germany

    Martin Gugat

Authors
  1. Martin Gugat
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Karl Kunisch

  2. Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. LS Angewandte Mathematik II Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91058, Erlangen, Germany

    Günter Leugering

  4. Institut für Mathematik Fak. II Mathematik & Naturwissenschaften, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Fredi Tröltzsch

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Gugat, M. (2009). Lavrentiev Prox-regularization Methods for Optimal Control Problems with Pointwise State Constraints. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Optimal Control of Coupled Systems of Partial Differential Equations. International Series of Numerical Mathematics, vol 158. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8923-9_8

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