Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93288
Title: | Lipschitz-like property relative to a set and the generalized Mordukhovich criterion | Authors: | Meng, KW Li, MH Yao, WF Yang, XQ |
Issue Date: | Sep-2021 | Source: | Mathematical programming, Sept. 2021, v. 189, no. 1-2, p. 455-489 | Abstract: | In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued mapping to have the Lipschitz-like property relative to a closed set by employing regular normal cone and limiting normal cone of a restricted graph of the set-valued mapping. We will obtain a complete characterization for a set-valued mapping to have the Lipschitz-property relative to a closed and convex set by virtue of the projection of the coderivative onto a tangent cone. Furthermore, by introducing a projectional coderivative of set-valued mappings, we establish a verifiable generalized Mordukhovich criterion for the Lipschitz-like property relative to a closed and convex set. We will study the representation of the graphical modulus of a set-valued mapping relative to a closed and convex set by using the outer norm of the corresponding projectional coderivative value. For an extended real-valued function, we will apply the obtained results to investigate its Lipschitz continuity relative to a closed and convex set and the Lipschitz-like property of a level-set mapping relative to a half line. | Keywords: | Graphical modulus Level-set mapping Lipschitz-like property relative to a set Mordukhovich criterion Projectional coderivative |
Publisher: | Springer | Journal: | Mathematical programming | ISSN: | 0025-5610 | DOI: | 10.1007/s10107-020-01568-0 | Rights: | © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020 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/s10107-020-01568-0 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Yao_Lipschitz-Like_Property_Relative.pdf | Pre-Published version | 762.83 kB | Adobe PDF | View/Open |
Page views
53
Last Week
0
0
Last month
Citations as of May 5, 2024
Downloads
46
Citations as of May 5, 2024
SCOPUSTM
Citations
3
Citations as of Apr 26, 2024
WEB OF SCIENCETM
Citations
3
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.