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Nonlinear Metric Subregularity

Alexander Y. Kruger (a.kruger***at***federation.edu.au)

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 A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, 1 (2015) 49-79. 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.

Keywords: error bounds; slope; metric regularity; metric subregularity; Holder metric subregularity; calmness

Category 1: Convex and Nonsmooth Optimization

Citation: Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-015-0807-8

Download: [PDF]

Entry Submitted: 02/21/2015
Entry Accepted: 02/22/2015
Entry Last Modified: 09/25/2015

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