Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applicati...

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Bibliographic Details
Published in:Optimization Vol. 74; no. 11; pp. 2577 - 2610
Main Authors: Mordukhovich, Boris S., Wu, Pengcheng, Yang, Xiaoqi
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 18.08.2025
Taylor & Francis LLC
Subjects:
Banach spaces
calculus rules
Constraints
Differentiation
normal cones and coderivatives
relative Lipschitzian stability
Stability criteria
Variational analysis
well-posedness
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applications. Our tools of generalized differentiation revolve around the newly introduced concept of ε-regular normal cone to sets and associated coderivative notions for set-valued mappings. Based on these constructions, we establish several characterizations of the central stability notion known as the relative Lipschitz-like property of set-valued mappings in infinite dimensions. Applying a new version of the constrained extremal principle of variational analysis, we develop comprehensive sum and chain rules for our major constructions of conic contingent coderivatives for multifunctions between appropriate classes of Banach spaces.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2385643