Mathematical Programming

, Volume 139, Issue 1–2, pp 223–242 | Cite as

Nonlinear regularity models

  • Alexander D. IoffeEmail author
Full Length Paper Series B


The paper studies regularity properties of set-valued mappings between metric spaces. In the context of metric regularity, nonlinear models correspond to nonlinear dependencies of estimates of error bounds in terms of residuals. Among the questions addressed in the paper are equivalence of the corresponding concepts of openness and “pseudo-Hölder” behavior, general and local regularity criteria with special emphasis on “regularity of order \(k\)”, for local settings, and variational methods to extimate regularity moduli in case of length range spaces. The majority of the results presented in the paper are new.


Metric regularity Regularity criterion Regularity of order \(k\)  Error bound Length space 

Mathematics Subject Classification (2000)

47H04 49J53 90C31 



I wish to express my thanks to the reviewers for the detailed analysis of the text and many good suggestions.


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© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013

Authors and Affiliations

  1. 1.Department of Mathematics, TechnionHaifaIsrael

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