On the Aubin property of a class of parameterized variational systems

The paper deals with a new sharp condition ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class encompasses various types of parameterized variational inequalities/generalized equations with fairly general constraint sets. The new condition require...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 86; no. 3; pp. 443 - 467
Main Authors: Gfrerer, H., Outrata, J. V.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects:
Business and Management
Calculus
Calculus of Variations and Optimal Control; Optimization
Constraining
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Original Article
Parameterization
90C31
49J53
90C46
Solution map
Aubin property
Graphical derivative
Directional limiting coderivative
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary:The paper deals with a new sharp condition ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class encompasses various types of parameterized variational inequalities/generalized equations with fairly general constraint sets. The new condition requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-017-0596-y