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. The equivalent relations between a solution of SVVLIs and MVVLIs, and a generalized weakly efficient solution of vector optimization problems are established under the assumptions of generalized pseudoconvexity and generalized invexity in the sense of the Clarke generalized directional derivative.
generalised weak cone-pseudomonotonicity
scientific article; zbMATH DE number 5586820
scientific article