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On strong duality in linear copositive programming

Author

Listed:
  • O. I. Kostyukova

    (Institute of Mathematics, National Academy of Sciences of Belarus)

  • T. V. Tchemisova

    (University of Aveiro, Campus Universitário Santiago)

Abstract

The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem satisfies the strong duality relations and does not require any additional regularity assumptions such as constraint qualifications. The main difference with the previously obtained results consists in the fact that now the extended dual problem uses neither the immobile indices themselves nor the explicit information about the convex hull of these indices. The strong duality formulations presented in the paper for linear copositive problems have similar structure and properties as that proposed in the works by M. Ramana, L. Tuncel, and H. Wolkowicz, for semidefinite programming.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-00995-3
    DOI: 10.1007/s10898-021-00995-3
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    References listed on IDEAS

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    1. 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.
    2. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1997. "Duality Results for Conic Convex Programming," Econometric Institute Research Papers EI 9719/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. 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.
    4. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
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    Cited by:

    1. Panos M. Pardalos & Michael Khachay & Yuri Kochetov, 2022. "Special Issue: 18th International conference on mathematical optimization theory and operations research (MOTOR 2019)," Journal of Global Optimization, Springer, vol. 83(3), pages 403-404, July.

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