Xian Jun Long and Jian Wen Peng Chongqing Technology and Business University, Chongqing Normal University
Abstract : In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. $\bf 133$ (2007), 151--161].