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Nonlinear Metric Subregularity

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Abstract

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.

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Acknowledgments

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.

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The author declares that he has no conflict of interest.

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  1. Centre for Informatics and Applied Optimization, Faculty of Science and Technology, Federation University Australia, POB 663, Ballarat, VIC, 3350, Australia

    Alexander Y. Kruger

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  1. Alexander Y. Kruger
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Correspondence to Alexander Y. Kruger.

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Kruger, A.Y. Nonlinear Metric Subregularity. J Optim Theory Appl 171, 820–855 (2016). https://doi.org/10.1007/s10957-015-0807-8

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