Robust error bounds for uncertain convex inequality systems with applications

Abstract

In this paper, we devote ourselves to studying robust error bounds for a convex inequality system in the face of data uncertainty. Under the assumption that uncertain sets are convex compact, we present a sufficient condition for the existence of robust error bounds of the uncertain convex inequality system by means of the associated recession cone and recession functions. When the uncertain sets are only compact, we establish a necessary and sufficient condition for the uncertain convex inequality system to possess a robust error bound by the Ekeland variational principle. As an immediate application, we obtain robust error bounds for the uncertain convex polynomial inequality system.

Keywords:

• Uncertain convex inequality system
• robust error bound
• recession function
• Ekeland variational principle
• polynomial system

MATHEMATICS SUBJECT CLASSIFICATIONS (2020):

• 49J53
• 90C17
• 90C25
• 90C31

Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments and suggestions which have led to the improvement of the earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11471230].