On Gap Functions for Vector Variational Inequalities

  • Guang-ya Chen
  • Chuen-Jin Goh
  • Xiao Qi Yang

Abstract

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 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Guang-ya Chen
    • 1
  • Chuen-Jin Goh
    • 2
  • Xiao Qi Yang
    • 3
  1. 1.Institute of Systems ScienceChinese Academy of SciencesBeijingP.R. China
  2. 2.Department of Mathematics and StatisticsUniversity of Western AustraliaNedlandAustralia
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloon, Hong KongChina

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