Vector variational-like inequalities with generalized bifunctions defined on nonconvex sets

In this paper, the nonemptiness and compactness of solution sets for Stampacchia vector variational-like inequalities (for short, SVVLIs) and Minty vector variational-like inequalities (for short, MVVLIs) with generalized bifunctions defined on nonconvex sets are investigated by introducing the concepts of generalized weak cone-pseudomonotonicity and generalized (proper) cone-suboddness. Moreover, some equivalent relations between a solution of SVVLIs and MVVLIs, and a generalized weakly efficient solution of vector optimization problems (for short, VOPs) are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of Clarke generalized directional derivative. These results extend and improve the corresponding results of others. (C) 2009 Elsevier Ltd. All rights reserved.