On applications of the calmness moduli for multifunctions to error bounds

Abstract

In this paper, we mainly study applications of the calmness moduli for multifunctions to error bounds of several non-convex systems. Based on the work given in Shen et al. [Calmness and the Abadie CQ for multifunctions and linear regularity for a collection of closed sets. SIAM J Optim. 2019;29(3):2291–2319], we use results on the calmness modulus of the multifunction therein to study error bounds of differentiable inclusions, weak sharp minima of a lower semicontinuous function and linear regularity of finitely many closed subsets. Several primal equivalent conditions for these regularity properties of the corresponding non-convex systems are provided with some mild assumptions.

Keywords:

• Calmness
• error bounds
• weak sharp minima
• linear regularity
• Shapiro property

2010 Mathematics Subject Classifications:

• 90C31
• 90C25
• 49J52
• 46B20

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant no. 11971422], CAS ‘Light of West China’ Program, and the Fok Ying-Tung Education Foundation [grant no. 151101], and by Joint Key Project of Yunnan Provincial Science and Technology Department and Yunnan University [No. 2018FY001(-014)] and IRTSTYN.