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

Xiao-Bing Li (), Suliman Al-Homidan (), Qamrul Hasan Ansari () and Jen-Chih Yao ()
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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
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 6, 785-802

Abstract: 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.

Keywords: Robust Farkas-Minkowski constraint qualification; Robust global error bound; Convex inequality system under data uncertainty; Epigraph of conjugate function; 49J99; 90C46; 90C31; 65K10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01679-w

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