- Title
- On the Aubin property of solution maps to parameterized variational systems with implicit constraints
- Creator
- Gfrerer, Helmut; Outrata, Jiri
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/174336
- Identifier
- vital:14824
- Identifier
-
https://doi.org/10.1080/02331934.2019.1657427
- Identifier
- ISBN:0233-1934 (ISSN)
- Abstract
- 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. © 2019, © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.; The research of the first author was supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of the second author was supported by the Grant Agency of the Czech Republic, Project 17-04301S and the Australian Research Council, Project 10.13039/501100000923DP160100854.
- Publisher
- Taylor and Francis Ltd.
- Relation
- Optimization Vol. 69, no. 7-8 (2020), p. 1681-1701; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Metadata is freely available under a CCO license
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
- Rights
- Open Access
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 49J53; 90C31; 90C46; Aubin property; directional limiting coderivative; parameterized variational system; Solution map
- Full Text
- Reviewed
- Funder
- The research of the first author was supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of the second author was supported by the Grant Agency of the Czech Republic, Project 17-04301S and the Australian Research Council, Project 10.13039/501100000923DP160100854.
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