On the Aubin property of solution maps to parameterized variational systems with implicit constraints. (2nd August 2020)

• Record Type: Journal Article
• Authors: Gfrerer, Helmut; Outrata, Jiří V.
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1681
• Page End: 1701
• Publication Date: 2020-08-02
• Subjects: Solution map -- parameterized variational system -- Aubin property -- directional limiting coderivative; 49J53 -- 90C31 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1657427
• Languages: English
• ISSNs: 0233-1934

Abstract

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.