On the Aubin property of solution maps to parameterized variational systems with implicit constraints

In the paper, a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems, the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g. parameter-dependent quasi-variational inequalit...

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Bibliographic Details
Published in:Optimization Vol. 69; no. 7-8; pp. 1681 - 1701
Main Authors: Gfrerer, Helmut, Outrata, Jiří V.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.08.2020
Taylor & Francis LLC
Subjects:
Aubin property
directional limiting coderivative
Parameterization
parameterized variational system
Parameters
Solution map
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In the paper, a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems, the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g. parameter-dependent quasi-variational inequalities and implicit complementarity problems. The result is based on a general condition ensuring the Aubin property of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative. Our final condition can be verified, however, without an explicit computation of these coderivatives. The procedure is illustrated by an example.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2019.1657427