Well-posedness for bilevel vector equilibrium problems with variable domination structures

Abstract

In this article, well-posedness for two types of bilevel vector equilibrium problems with variable domination structures are introduced and studied. With the help of cosmically upper continuity or Hausdorff upper semi-continuity for variable domination structures, sufficient and necessary conditions are given for such problems to be Levitin-Polyak (LP) well-posed and LP well-posedness in the generalized sense. As variable domination structure is a valid generalization of fixed one, the main results obtained in this article extend and develop some recent works in the literature.

Keywords

• bilevel vector equilibrium problem
• variable domination structures
• well-posedness
• cosmically upper continuity
• approximating solution sequence
• 49j40
• 90c33
• 47j20