Journal of Optimization Theory and Applications

, Volume 171, Issue 3, pp 820–855 | Cite as

Nonlinear Metric Subregularity

  • Alexander Y. Kruger


In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in Kruger (Error bounds and metric subregularity. Optimization 64(1):49–79, 2015). Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.


Error bounds Slope Metric regularity Metric subregularity Hölder metric subregularity Calmness 

Mathematics Subject Classification

49J52 49J53 58C06 47H04 54C60 



The research was supported by the Australian Research Council, Project DP11010 2011. The author wishes to thank two of the three anonymous referees for the careful reading of the manuscript and many constructive comments and suggestions.

Conflict of interest

The author declares that he has no conflict of interest.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Centre for Informatics and Applied Optimization, Faculty of Science and TechnologyFederation University AustraliaBallaratAustralia

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