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A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate

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Abstract

In this paper, a systematic study of the strong metric subregularity property of mappings is carried out by means of a variational tool, called steepest displacement rate. With the aid of this tool, a simple characterization of strong metric subregularity for multifunctions acting in metric spaces is formulated. The resulting criterion is shown to be useful for establishing stability properties of the strong metric subregularity in the presence of perturbations, as well as for deriving various conditions, enabling one to detect such a property in the case of nonsmooth mappings. Some of these conditions, involving several nonsmooth analysis constructions, are then applied in studying the isolated calmness property of the solution mapping to parameterized generalized equations.

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Acknowledgments

The author thanks both the anonymous referees for their valuable remarks and comments.

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  1. Department of Mathematics and Applications, University of Milano-Bicocca, Milan, Italy

    Amos Uderzo

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  1. Amos Uderzo
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Correspondence to Amos Uderzo.

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Communicated by Hedy Attouch.

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Uderzo, A. A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate. J Optim Theory Appl 171, 573–599 (2016). https://doi.org/10.1007/s10957-016-0952-8

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