We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities.
Published in Constructive Nonsmooth Analysis and Related Topics (Vladimir Demyanov, Panos M. Pardalos, and Mikhail Batsyn, eds.) Springer Optimization and Its Applications, Vol. 87. Springer-Verlag, Berlin, 2014, 157-172