Saddle points and gap functions for vector equilibrium problems via conjugate duality in vector optimization (Q924222)

Given a (primal) constrained vector minimization problem where weak efficiency is considered, two conjugate dual problems are introduced: the so-called Lagrange and the Fenchel-Lagrange dual problems. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problems are established. In addition, two set-valued gap functions for a vector equilibrium problem by virtue of conjugate dual problems are considered.