- Title
- Primal Characterizations of error bounds for composite-convex inequalities
- Creator
- Wei, Zhou; Théra, Michel; Yao, Jen-Chih
- Date
- 2023
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/198716
- Identifier
- vital:19094
- Identifier
- ISSN:0944-6532 (ISSN)
- Abstract
- This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions for error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping is metrically regular at the given point. The accurate estimate on the error bound modulus is also obtained. © 2023 Heldermann Verlag. All rights reserved.
- Publisher
- Heldermann Verlag
- Relation
- Journal of Convex Analysis Vol. 30, no. 4 (2023), p. 1329-1350
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2023 Heldermann Verlag
- Rights
- Open Access
- Subject
- 4904 Pure mathematics; Bouligand tangent cone; composite-convex inequality; Error bound; Hausdorff-Pompeiu excess; lower Hadamard directional derivative
- Full Text
- Reviewed
- Funder
- Research of the first author was supported by the National Natural Science Foundations of China(Grant Nos. 11971422 and 12171419), and funded by Science and Technology Project of Hebei Education Department (No. ZD2022037) and the Natural Science Foundation of Hebei Province(A2022201002). Research of the second author benefited from the support of the FMJH Program PGMO and from the support of EDF as well as from the FJMH Program Gaspard Monge for optimization and operation research and their interactions with data sciences, and was supported by a public grant as part of the investissement d'avenir project, reference ANR-11-LABEX-0056-LMH, LabEx LMH.
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