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Copositive Programming via Semi-Infinite Optimization

Author

Listed:
  • Faizan Ahmed

    (University of Twente)

  • Mirjam Dür

    (University of Trier)

  • Georg Still

    (University of Twente)

Abstract

Copositive programming (CP) can be regarded as a special instance of linear semi-infinite programming (SIP). We study CP from the viewpoint of SIP and discuss optimality and duality results. Different approximation schemes for solving CP are interpreted as discretization schemes in SIP. This leads to sharp explicit error bounds for the values and solutions in dependence on the mesh size. Examples illustrate the structure of the original program and the approximation schemes.

Suggested Citation

  • Faizan Ahmed & Mirjam Dür & Georg Still, 2013. "Copositive Programming via Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 322-340, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0344-2
    DOI: 10.1007/s10957-013-0344-2
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    References listed on IDEAS

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    1. Immanuel Bomze & Werner Schachinger & Gabriele Uchida, 2012. "Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 423-445, March.
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    Cited by:

    1. Xiaolong Kuang & Luis F. Zuluaga, 2018. "Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization," Journal of Global Optimization, Springer, vol. 70(3), pages 551-577, March.
    2. O. I. Kostyukova & T. V. Tchemisova, 2022. "On strong duality in linear copositive programming," Journal of Global Optimization, Springer, vol. 83(3), pages 457-480, July.
    3. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    4. Mirjam Dür & Bolor Jargalsaikhan & Georg Still, 2017. "Genericity Results in Linear Conic Programming—A Tour d’Horizon," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 77-94, January.
    5. Olga Kostyukova & Tatiana Tchemisova, 2017. "Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 76-103, October.

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