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.
Highlights
The Aubin (Lipschitz-like) property is probably the most important extension of the Lipschitz continuity to multifunctions
In the form (1), we can write down a large class of parameterized optimization and equilibrium problems and so this condition can well be used, e.g. in post-optimal analysis or in problems with the so-called equilibrium constraints
→A means the convergence within a set A and Lim sup stands for the Painlevé–Kuratowski set limit
Summary
To cite this article: Helmut Gfrerer & Jiří V. Outratab,c aInstitute of Computational Mathematics, Johannes Kepler University Linz, Linz, Austria; bInstitute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic; cCentre for Informatics and Applied Optimization, Federation University of Australia, Ballarat, Australia
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