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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.

On applications of the calmness moduli for multifunctions to error bounds