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Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques

Author

Listed:
  • Ionela Prodan

    (SUPELEC Systems Sciences (E3S)
    CNRS-SUPELEC)

  • Florin Stoican

    (Norwegian University of Science and Technology)

  • Sorin Olaru

    (SUPELEC Systems Sciences (E3S))

  • Silviu-Iulian Niculescu

    (CNRS-SUPELEC)

Abstract

This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered.

Suggested Citation

  • Ionela Prodan & Florin Stoican & Sorin Olaru & Silviu-Iulian Niculescu, 2012. "Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 549-572, August.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0022-9
    DOI: 10.1007/s10957-012-0022-9
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    Citations

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    Cited by:

    1. Vinícius Antonio Battagello & Nei Yoshihiro Soma & Rubens Junqueira Magalhães Afonso, 2020. "Computational load reduction of the agent guidance problem using Mixed Integer Programming," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-45, June.
    2. Joey Huchette & Joey Huchette, 2019. "A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 793-820, August.
    3. Rubens J. M. Afonso & Roberto K. H. Galvão, 2014. "Comments on “Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques”," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 996-1003, September.

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