Affine Variational Inequalities on Normed Spaces

  • Nguyen Dong YenEmail author
  • Xiaoqi Yang


This paper studies infinite-dimensional affine variational inequalities on normed spaces. It is shown that infinite-dimensional quadratic programming problems and infinite-dimensional linear fractional vector optimization problems can be studied by using affine variational inequalities. We present two basic facts about infinite-dimensional affine variational inequalities: the Lagrange multiplier rule and the solution set decomposition.


Infinite-dimensional affine variational inequality Infinite-dimensional quadratic programming Infinite-dimensional linear fractional vector optimization Generalized polyhedral convex set Solution set 

Mathematics Subject Classification

49J40 49J50 49K40 90C20 90C29 



The first author was supported by the joint research project from RFBR and VAST.HTQT.NGA-02/16-17. The second author was supported by the Research Grants Council of Hong Kong (PolyU 152167/15E). The authors would like to thank Professor Franco Giannessi for his helpful comments and suggestions.


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Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Department of Applied Mathematics, The Hong Kong Polytechnic UniversityHong KongChina

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