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On the Uniform Duality in Copositive Optimization

Author

Listed:
  • O. I. Kostyukova

    (National Academy of Sciences of Belarus)

  • T. V. Tchemisova

    (University of Aveiro)

  • O. S. Dudina

    (Belarusian State University)

Abstract

In this paper, we establish new necessary and sufficient conditions guaranteeing the uniform LP duality for linear problems of Copositive Programming and formulate these conditions in different equivalent forms. The main results are obtained using the approach developed in previous papers of the authors and based on a concept of immobile indices that permits alternative representations of the set of feasible solutions.

Suggested Citation

  • O. I. Kostyukova & T. V. Tchemisova & O. S. Dudina, 2024. "On the Uniform Duality in Copositive Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1940-1966, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02515-1
    DOI: 10.1007/s10957-024-02515-1
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    References listed on IDEAS

    as
    1. O. I. Kostyukova & T. V. Tchemisova & S. A. Yermalinskaya, 2010. "Convex Semi-Infinite Programming: Implicit Optimality Criterion Based on the Concept of Immobile Indices," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 325-342, May.
    2. Qinghong Zhang, 2024. "Understanding Badly and Well-Behaved Linear Matrix Inequalities Via Semi-infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1820-1846, November.
    3. Qinghong Zhang, 2008. "Uniform LP duality for semidefinite and semi-infinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 205-213, June.
    4. Gábor Pataki, 2007. "On the Closedness of the Linear Image of a Closed Convex Cone," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 395-412, May.
    5. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    6. V. Jeyakumar, 2008. "Constraint Qualifications Characterizing Lagrangian Duality in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 31-41, January.
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