Gap Function for Set-Valued Vector Variational-Like Inequalities

  • S. K. Mishra
  • S. Y. Wang
  • K. K. Lai


Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities (VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem.


Vector variational-like inequalities Set-valued mappings Gap functions Existence of a solution Semidefinite programming 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, College of Basic Sciences and HumanitiesG.B. Pant University of Agriculture and TechnologyPantnagarIndia
  2. 2.City University of Hong KongDepartment of Management SciencesKowloonHong Kong
  3. 3.Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingChina

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