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Parabolic optimal control problems with combinatorial switching constraints, part III: branch-and-bound algorithm

Author

Listed:
  • Christoph Buchheim

    (TU Dortmund University)

  • Alexandra Grütering

    (TU Dortmund University)

  • Christian Meyer

    (TU Dortmund University)

Abstract

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given tolerance $$\varepsilon >0$$ ε > 0 , we show how to compute in finite time an $$\varepsilon $$ ε -optimal solution in function space, independently of any prior discretization. The main ingredients in our approach are an appropriate branching strategy in infinite dimension, an a posteriori error estimation in order to obtain safe dual bounds, and an adaptive refinement strategy in order to allow arbitrary switching points in the limit. The performance of our approach is demonstrated by extensive experimental results.

Suggested Citation

  • Christoph Buchheim & Alexandra Grütering & Christian Meyer, 2025. "Parabolic optimal control problems with combinatorial switching constraints, part III: branch-and-bound algorithm," Computational Optimization and Applications, Springer, vol. 90(3), pages 649-689, April.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:3:d:10.1007_s10589-025-00654-3
    DOI: 10.1007/s10589-025-00654-3
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    References listed on IDEAS

    as
    1. Sebastian Sager & Michael Jung & Christian Kirches, 2011. "Combinatorial integral approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(3), pages 363-380, June.
    2. Veronika Karl & Daniel Wachsmuth, 2018. "An augmented Lagrange method for elliptic state constrained optimal control problems," Computational Optimization and Applications, Springer, vol. 69(3), pages 857-880, April.
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