Error Bounds in Metric Spaces and Application to the Perturbation Stability of Metric Regularity
Huynh Van Ngai, Michel A. Théra · SIAM Journal on Optimization · 2008
This paper was motivated by the need to establish some new characterizations of the metric regularity of set-valued mappings. Through these new characterizations it was possible to investigate the global/local perturbation stability of the metric regularity and to extend a result by Ioffe [Set-Valued Anal., 9 (2001), pp. 101–109] on the perturbation stability of the global metric regularity when the image space is not necessarily complete. It was also possible to give a characterization of the local metric regularity and to derive a local version of the perturbation stability of the metric regularity. In this work we also describe an application of this perturbation stability and give a simple proof of a result on the error bound of 2-regular mappings established by Izmailov and Solodov [Math. Program., 89 (2001), pp. 413–435] and generalized by He and Sun [Math. Oper. Res., 30 (2005), pp. 701–717].