Vector Variational Inequalities and Vector Equilibria

Volume 38 of the series Nonconvex Optimization and Its Applications pp 55-72

On Gap Functions for Vector Variational Inequalities

  • Guang-ya ChenAffiliated withInstitute of Systems Science, Chinese Academy of Sciences
  • , Chuen-Jin GohAffiliated withDepartment of Mathematics and Statistics, University of Western Australia
  • , Xiao Qi YangAffiliated withDepartment of Applied Mathematics, The Hong Kong Polytechnic University


We extend the theory of gap functions for scalar variational inequality problems (see [1,8]) to the case of vector variational inequality. The gap functions for vector variational inequality are defined as set-valued mappings. The significance of the gap function is interpreted in terms of the inverse vector variational inequality. Convexity properties of these set-valued mappings are studied under different assumptions.

Key Words

Vector variational inequality gap functions duality Fenchel conjugate