Multiobjective variational problems and generalized vector variational-type inequalities

The purpose of this paper is to generalize the vector variational‐type inequalities, formulated by Kim [J. Appl. Math. Comput. 16 (2004) 279–287], by setting the norms into Minty and Stampacchia forms. We also demonstrate the relationships between these generalized inequalities and multiobjective variational problems, by using the notions of strongly convex functionals. The theoretical developments are illustrated through numerical examples.