This paper is concerned with gap functions of generalized vector variational inequalities (GVVI). By using scalarization approach, scalar-valued variational inequalities of (GVVI) are introduced. Some relationships between the solutions of (GVVI) and its scalarized versions are established. Then, by using these relationships and some mild conditions, scalar-valued gap functions for (GVVI) are established.
"A Note on Scalar-Valued Gap Functions for Generalized Vector Variational Inequalities." Abstr. Appl. Anal. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/492103