Computational Optimization and Applications

, Volume 37, Issue 1, pp 67-81

First online:

Solving variational inequalities defined on a domain with infinitely many linear constraints

  • Shu-Cherng FangAffiliated withDepartment of Industrial Engineering and Operations Research Program, North Carolina State UniversityDepartments of Mathematical Sciences and Industrial Engineering Program, Tsinghua University Email author 
  • , Soonyi WuAffiliated withInstitute of Applied Mathematics, National Cheng Kung UniversityNational Center for Theoretical Sciences
  • , Ş. İlker BirbilAffiliated withFaculty of Engineering and Natural Sciences, Sabanci University

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We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods.


Variational inequality problem Analytic center based cutting plane method Discretization method Semi-infinite programming