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

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  • X. X. Huang

    (Chongqing University)

  • Y. P. Fang

    (Sichuan University)

  • X. Q. Yang

    (The Hong Kong Polytechnic University)

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.

Suggested Citation

  • X. X. Huang & Y. P. Fang & X. Q. Yang, 2014. "Characterizing the Nonemptiness and Compactness of the Solution Set of a Vector Variational Inequality by Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 548-558, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-012-0224-1
    DOI: 10.1007/s10957-012-0224-1
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    References listed on IDEAS

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    1. S. Deng, 1998. "Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 123-131, January.
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    Cited by:

    1. Ren-you Zhong & Zhen Dou & Jiang-hua Fan, 2015. "Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 527-549, November.
    2. Jiang-hua Fan & Yan Jing & Ren-you Zhong, 2015. "Nonemptiness and boundedness of solution sets for vector variational inequalities via topological method," Journal of Global Optimization, Springer, vol. 63(1), pages 181-193, September.

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