Relative Lipschitz-like property of parametric systems via projectional coderivative

This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Yao, Wenfang, Yang, Xiaoqi
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 20.10.2022
Subjects:	Combinatorial analysis Domains Estimates Mapping Mathematical analysis
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	This paper concerns upper estimates of the projectional coderivative of implicit mappings and corresponding applications on analyzing the relative Lipschitz-like property. Under different constraint qualifications, we provide upper estimates of the projectional coderivative for solution mappings of parametric systems. For the solution mapping of affine variational inequalities, a generalized critical face condition is obtained for sufficiency of its Lipschitz-like property relative to a polyhedral set within its domain under a constraint qualification. The equivalence between the relative Lipschitz-like property and the local inner-semicontinuity for polyhedral multifunctions is also demonstrated. For the solution mapping of linear complementarity problems with a \(Q_0\)-matrix, we establish a sufficient and necessary condition for the Lipschitz-like property relative to its convex domain via the generalized critical face condition and its combinatorial nature.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2210.11335