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Journal of Optimization Theory and Applications

, Volume 154, Issue 2, pp 549–572 | Cite as

Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques

  • Ionela Prodan
  • Florin Stoican
  • Sorin Olaru
  • Silviu-Iulian Niculescu
Article

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.

Keywords

Mixed integer programming (MIP) Not convex constraints Hyperplane arrangements Cell merging 

Notes

Acknowledgements

The research of Ionela Prodan is financially supported by the EADS Corporate Foundation (091-AO09-1006). Florin Stoican’s work was carried out in Supelec, during the tenure of a CARNOT C3S fellowship. The authors would like to thank Professor Panos M. Pardalos, as well as the anonymous reviewers for their useful comments and remarks that helped in improving the overall presentation of this paper.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Ionela Prodan
    • 1
    • 3
  • Florin Stoican
    • 2
  • Sorin Olaru
    • 1
  • Silviu-Iulian Niculescu
    • 3
  1. 1.Automatic Control DepartmentSUPELEC Systems Sciences (E3S)Gif sur YvetteFrance
  2. 2.Department of Engineering CyberneticsNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Laboratory of Signal and SystemsCNRS-SUPELECGif sur YvetteFrance

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