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

0509759 - ÚTIA 2021 RIV DE eng J - Journal Article
Gfrerer, H. - Outrata, Jiří
On the Aubin property of solution maps to parameterized variational systems with implicit constraints.
Optimization. Roč. 69, 7-8 (2020), s. 1681-1701. ISSN 0233-1934. E-ISSN 1029-4945
R&D Projects: GA ČR GA17-04301S
Institutional support: RVO:67985556
Keywords : solution map * parameterized variational system * Aubin property * directional limiting coderivative
OECD category: Pure mathematics
Impact factor: 2.360, year: 2020
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2019/MTR/outrata-0509759.pdf https://www.tandfonline.com/doi/full/10.1080/02331934.2019.1657427

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.
Permanent Link: http://hdl.handle.net/11104/0300390