By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition for ε-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separation functional, a necessary and sufficient condition for ε-vector equilibrium problem without constraints is obtained.
Lu Wei-zhong. Huang Shou-jun. Yang Jun. "Optimality Conditions for ε -Vector Equilibrium Problems." Abstr. Appl. Anal. 2014 (SI19) 1 - 4, 2014. https://doi.org/10.1155/2014/509404