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On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions

Author

Listed:
  • Paul Manns

    (Faculty of Mathematics, TU Dortmund University, 44227 Dortmund, Germany)

  • Marvin Severitt

    (Faculty of Mathematics, TU Dortmund University, 44227 Dortmund, Germany)

Abstract

We analyze integer linear programs that we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness of the discretized problems and the connection to graph-based problems. We show that the underlying polyhedron exhibits structural restrictions in its vertices with regard to which variables can attain fractional values at the same time. Based on this property, we derive cutting planes by employing a relation to shortest-path and minimum bisection problems. We propose a branching rule and a primal heuristic which improves previously found feasible points. We validate the proposed tools with a numerical benchmark in a standard integer programming solver. We observe a significant speedup for medium-sized problems. Our results give hints for scaling toward larger instances in the future.

Suggested Citation

  • Paul Manns & Marvin Severitt, 2025. "On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions," INFORMS Journal on Computing, INFORMS, vol. 37(4), pages 1121-1141, July.
    • Handle: RePEc:inm:orijoc:v:37:y:2025:i:4:p:1121-1141
    DOI: 10.1287/ijoc.2024.0680
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    References listed on IDEAS

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    1. Marvin Severitt & Paul Manns, 2023. "Efficient Solution of Discrete Subproblems Arising in Integer Optimal Control with Total Variation Regularization," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 869-885, July.
    2. 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.
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