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

Amos Uderzo ()
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Amos Uderzo: University of Milano-Bicocca

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 14, 573-599

Abstract: 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.

Keywords: Strong metric subregularity; Steepest descent rate; Sharp minimality; Isolated calmness; Injectivity constant; First-order $$\epsilon $$ ϵ -approximation; Outer prederivative; Generalized equation; 49J53; 49J52; 90C48 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0952-8

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