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Quasi-Strict Feasibility of Generalized Mixed Variational Inequalities in Reflexive Banach Spaces

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  • Xue-ping Luo

    (Southwest University for Nationalities)

Abstract

In this paper, quasi-strict feasibility of a generalized mixed variational inequality as a new notation is introduced, which is weaker than its strict feasibility and recovers the existing concept of strict feasibility for a generalized variational inequality. By using the equivalent characterization of the nonemptiness and boundedness of the solution set for the generalized mixed variational inequality, it is proved that quasi-strict feasibility is a sufficient condition for the generalized mixed variational inequality with a f-pseudomonotone and upper hemicontinuous mapping to have a nonempty and bounded solution set in reflexive Banach spaces. Our results generalize and extend some known results in Zhong and Huang (J Optim Theory Appl 152(3):696–709, 2012).

Suggested Citation

  • Xue-ping Luo, 2018. "Quasi-Strict Feasibility of Generalized Mixed Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 439-454, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1278-5
    DOI: 10.1007/s10957-018-1278-5
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    References listed on IDEAS

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    1. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.
    2. F. Q. Xia & N. J. Huang, 2009. "Auxiliary Principle and Iterative Algorithms for Lions-Stampacchia Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 377-389, February.
    3. Ren-you Zhong & Nan-jing Huang, 2012. "Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 696-709, March.
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    1. Ren-you Zhong & Nan-jing Huang, 2012. "Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 696-709, March.

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