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Affine Variational Inequalities on Normed Spaces

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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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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Nguyen Dong Yen

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Xiaoqi Yang

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  1. Nguyen Dong Yen
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  2. Xiaoqi Yang
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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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  • DOI: https://doi.org/10.1007/s10957-018-1296-3

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