Abstract: We discussed the optimal conditions for lower semicontionuity of efficient solutions to parametric set-valued vector equilibrium problem in real Hausdorff topological vector space. Firstly, we gave the concepts of weak efficient solution,Henig efficient solution,Global efficient solution, super efficient solution and f-efficient solution for the parametric set-valued vector equilibrium problem. Secondly, on the basis of nearly cone-subconvexlike, we gave the characterization results of weak efficient solution, Henig efficient solution, Global efficient solution and super efficient solution by using the form of f-efficient solution and the separation theorem of convex sets. Finally, we established the optimality theorems of lower semicontinuity for the efficient solutions to parametric setvalued vector equilibrium problem under the weak-f-property of set-valued mapping.

Key words: efficient solution, lower semicontionuity, optimality, nearly cone-subconvexlike set-valued mapping, parametric set-valued vector, equilibrium problem