Error bounds revisited

We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuit...

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Bibliographic Details
Published inOptimization Vol. 71; no. 4; pp. 1021 - 1053
Main Authors Cuong, Nguyen Duy, Kruger, Alexander Y.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2022
Taylor & Francis LLC
Subjects
Convexity
Error bound
Metric space
Operators (mathematics)
semi-infinite programming
slope
subdifferential
subregularity
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Summary:We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuity in the case of sufficient conditions and (in some cases) convexity in the case of necessary conditions. We expose the roles of the assumptions involved in the error bound assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. Employing special collections of slope operators, we introduce a succinct form of sufficient error bound conditions, which allows one to combine in a single statement several different assertions: nonlocal and local primal space conditions in complete metric spaces, and subdifferential conditions in Banach and Asplund spaces.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2032695