Continuity properties of solution maps of parametric lexicographic equilibrium problems

Abstract

Inspired by the great importance of equilibrium problems and the lexicographic order, we consider a parametric lexicographic equilibrium problem. Sufficient conditions for the upper semicontinuity, closedness, and continuity of solution maps are established. Many examples are provided to ensure the essentialness of the imposed assumptions. Applications to lexicographic variational inequalities and lexicographic optimization problems are discussed.