Affine Variational Inequalities on Normed Spaces

Abstract

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.

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Acknowledgements

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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Correspondence to Nguyen Dong Yen.

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Yen, N.D., Yang, X. Affine Variational Inequalities on Normed Spaces. J Optim Theory Appl 178, 36–55 (2018). https://doi.org/10.1007/s10957-018-1296-3

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Keywords

  • 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