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Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty

Author

Listed:
  • Xiao-Bing Li

    (Chongqing Jiaotong University)

  • Suliman Al-Homidan

    (King Fahd University of Petroleum and Minerals)

  • Qamrul Hasan Ansari

    (King Fahd University of Petroleum and Minerals
    Aligarh Muslim University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

The Farkas-Minkowski constraint qualification is an important concept within the theory and applications of mathematical programs with inequality constraints. In this paper, we mainly deal with the robust version of Farkas-Minkowski constraint qualification for convex inequality system under data uncertainty. We prove that the existence of robust global error bound is a sufficient condition for ensuring robust Farkas-Minkowski constraint qualification for convex inequality system in face of data uncertainty, where the uncertain data belong to a prescribed compact and convex uncertainty set. Moreover, we show that the converse is true for convex quadratic inequality system, when the uncertain data belong to a scenario uncertainty set.

Suggested Citation

  • Xiao-Bing Li & Suliman Al-Homidan & Qamrul Hasan Ansari & Jen-Chih Yao, 2020. "Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 785-802, June.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:3:d:10.1007_s10957-020-01679-w
    DOI: 10.1007/s10957-020-01679-w
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    References listed on IDEAS

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    1. A. Charnes & W. W. Cooper & K. Kortanek, 1965. "On Representations of Semi-Infinite Programs which Have No Duality Gaps," Management Science, INFORMS, vol. 12(1), pages 113-121, September.
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