Document Type : Research Paper

Authors

• Amir Mahdi Bornayoon ¹
• Hossein Mohebi ²

¹ Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran

² Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran

Abstract

In this paper, we study Lipschitz global error bounds for lower semi-continuous convex-along-rays (l.s.c. CAR) functions. We find a condition that ensures the existence of a global error bound for a CAR function. Moreover, we find a condition under which an l.s.c. CAR function does not have a Lipschitz global error bound. Finally, we survey Lipschitz's global error bounds of an l.s.c. (in particular, an l.s.c. CAR) function from the perspective of abstract convexity.

Keywords

• Convex-along-rays functions
• Global error bound
• Abstract convexity