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.
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Acknowledgements
This research was done during the visit of first and third author to King Fahd University of Petrol and Minerals (KFUPM), Dhahran, Saudi Arabia. First three authors are grateful to KFUPM for providing excellent research facilities to carry out their part of research work. The research of the first author was also supported by the Natural Science Foundation of Chongqing (cstc2019jcyj-msxmX0443) and the Preparatory Project of Chongqing Jiaotong University (2018PY22). The authors would like to express their deep gratitude to the anonymous referees and the associate editor for their valuable comments and suggestions, which helped to improve the paper.
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Communicated by Vaithilingam Jeyakumar.
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Li, XB., Al-Homidan, S., Ansari, Q.H. et al. Robust Farkas-Minkowski Constraint Qualification for Convex Inequality System Under Data Uncertainty. J Optim Theory Appl 185, 785–802 (2020). https://doi.org/10.1007/s10957-020-01679-w
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DOI: https://doi.org/10.1007/s10957-020-01679-w
Keywords
- Robust Farkas-Minkowski constraint qualification
- Robust global error bound
- Convex inequality system under data uncertainty
- Epigraph of conjugate function