Generalized Metric Subregularity for Generalized Subsmooth Multifunctions in Asplund Spaces

This paper introduces and considers the concept of generalized subsmoothness of a multifunction, which is a generalization of both the prox-regularity property and the subsmoothness property of multifunctions. Subsequently, it mainly deals with generalized metric subregularity (in particular, Hölder...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 33; no. 2; p. 14
Main Authors: Gao, Ming, Ouyang, Wei, Zhang, Jin, Zhu, Jiangxing
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2025
Springer Nature B.V
Subjects:
Analysis
Banach spaces
Mathematics
Mathematics and Statistics
Optimization
Quasi Newton methods
Research Article
90C31
Variational analysis
49J53
Hölder metric subregularity
Normal cone
49J52
Coderivative
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:This paper introduces and considers the concept of generalized subsmoothness of a multifunction, which is a generalization of both the prox-regularity property and the subsmoothness property of multifunctions. Subsequently, it mainly deals with generalized metric subregularity (in particular, Hölder metric subregularity) for general set-valued mappings in Asplund spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive sufficient conditions for generalized metric subregularity, which extend even the known results for the conventional metric subregularity. In particular, our results improve/extend the main results established by Li and Mordukhovich (SIAM J. Optim. 22:1655–1684, 2012 ). Moreover, we also conduct local convergence analysis of an inexact quasi-Newton method for solving the generalized equation 0 ∈ f ( x ) + F ( x ) in Banach spaces, where the function f is continuous but not smooth and F is a set-valued mapping with closed graph.
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-025-00753-7