On applications of the calmness moduli for multifunctions to error bounds. (2nd December 2022)

• Record Type: Journal Article
• Authors: Wei, Zhou; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 71:Number 12(2022)
• Page Start: 3647
• Page End: 3668
• Publication Date: 2022-12-02
• Subjects: Calmness -- error bounds -- weak sharp minima -- linear regularity -- Shapiro property; 90C31 -- 90C25 -- 49J52 -- 46B20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1906873
• Languages: English
• ISSNs: 0233-1934

Abstract

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.