An improved stability result on the metric regularity under Lipschitz set-valued perturbations

Metric regularity is an important concept in variational analysis. Perturbation analysis of metric regularity is studied in this paper. An improved stability result on the metric regularity under Lipschitz set-valued perturbations is established. Compared to the known results, the conditions are relaxed and the proof is provided more concisely. In other words, we allow the diameter of the image of the perturbation mapping at the reference point to vary in a larger domain, and give a simpler argument. An example is presented in which our result can be applied but not the known results. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper examines perturbation analysis of metric regularity, establishing an improved stability result under Lipschitz set-valued perturbations, with more relaxed conditions and a more concise proof compared to existing results.