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http://hdl.handle.net/10397/80844
Title: | On error bound moduli for locally Lipschitz and regular functions | Authors: | Li, MH Meng, KW Yang, XQ |
Issue Date: | Sep-2018 | Source: | Mathematical programming, Sept. 2018, v. 171, no. 1-2, p. 463-487 | Abstract: | In this paper we study local error bound moduli for a locally Lipschitz and regular function via outer limiting subdifferential sets. We show that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance from 0 to the outer limiting subdifferential set of a lower C1 function is equal to the local error bound modulus. | Keywords: | Error bound modulus Locally Lipschitz Outer limiting subdifferential Support function End set Lower C1 function |
Publisher: | Springer | Journal: | Mathematical programming | ISSN: | 0025-5610 | DOI: | 10.1007/s10107-017-1200-1 | Rights: | © Springer-Verlag GmbH Germany and Mathematical Optimization Society 2017 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10107-017-1200-1 |
Appears in Collections: | Journal/Magazine Article |
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Yang_Error_Bound_Moduli.pdf | Pre-Published version | 857.2 kB | Adobe PDF | View/Open |
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