Full Stability of General Parametric Variational Systems

The paper introduces and studies the notions of Lipschitzian and Hölderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 26; no. 4; pp. 911 - 946
Main Authors: Mordukhovich, B. S., Nghia, T. T. A., Pham, D. T.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2018
Springer Nature B.V
Subjects:
Analysis
Economic models
Hilbert space
Mathematics
Mathematics and Statistics
Optimization
Stability
Legendre forms
Variational analysis
Parametric variational systems
Polyhedricity
Subgradients
Variational inequalities and variational conditions
Primary 49J53
Lipschitzian and Hölderian full stability
Generalized differentiation
Secondary 49J52, 90C31
Prox-regularity
Coderivatives
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:The paper introduces and studies the notions of Lipschitzian and Hölderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability properties under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-018-0474-7