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Characterizing the Nonemptiness and Compactness of the Solution Set of a Vector Variational Inequality by Scalarization

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Abstract

In this paper, the nonemptiness and compactness of the solution set of a pseudomonotone vector variational inequality defined in a finite-dimensional space are characterized in terms of that of the solution sets of a family of linearly scalarized variational inequalities.

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Acknowledgements

The authors would like to thank the referees and the editor for their helpful comments and suggestions which have led to the improvement of the early version of this paper. The first author was supported by the National Science Foundation of China and a research grant from Chongqing University. The second author was partially supported by the Natural Science Foundation of China (11001187, 11201042). The third author was partially supported by the Research Grants Council of Hong Kong (PolyU 5306/11E).

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Authors and Affiliations

  1. School of Economics and Business Administration, Chongqing University, Chongqing, China

    X. X. Huang

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, P.R. China

    Y. P. Fang

  3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hum, Kowloon, Hong Kong

    X. Q. Yang

Authors
  1. X. X. Huang
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  2. Y. P. Fang
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  3. X. Q. Yang
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Correspondence to Y. P. Fang.

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Huang, X.X., Fang, Y.P. & Yang, X.Q. Characterizing the Nonemptiness and Compactness of the Solution Set of a Vector Variational Inequality by Scalarization. J Optim Theory Appl 162, 548–558 (2014). https://doi.org/10.1007/s10957-012-0224-1

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  • DOI: https://doi.org/10.1007/s10957-012-0224-1

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