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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Veröffentlicht in:Optimization Jg. 74; H. 11; S. 2577 - 2610
Hauptverfasser: Mordukhovich, Boris S., Wu, Pengcheng, Yang, Xiaoqi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis 18.08.2025
Taylor & Francis LLC
Schlagworte:
Banach spaces
calculus rules
Constraints
Differentiation
normal cones and coderivatives
relative Lipschitzian stability
Stability criteria
Variational analysis
well-posedness
ISSN:0233-1934, 1029-4945
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Abstract 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.
AbstractList 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.
Author Yang, Xiaoqi
Mordukhovich, Boris S.
Wu, Pengcheng
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  organization: Wayne State University
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  givenname: Pengcheng
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  organization: The Hong Kong Polytechnic University
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  givenname: Xiaoqi
  surname: Yang
  fullname: Yang, Xiaoqi
  organization: The Hong Kong Polytechnic University
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Snippet This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust...
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SubjectTerms Banach spaces
calculus rules
Constraints
Differentiation
normal cones and coderivatives
relative Lipschitzian stability
Stability criteria
Variational analysis
well-posedness
Title Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces
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