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Strict Feasibility for Generalized Mixed Variational Inequality in Reflexive Banach Spaces

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  • Ren-you Zhong

    (Sichuan University)

  • Nan-jing Huang

    (Sichuan University)

Abstract

The purpose of this paper is to investigate the nonemptiness and boundedness of solution set for a generalized mixed variational inequality with strict feasibility in reflexive Banach spaces. A concept of strict feasibility for the generalized mixed variational inequality is introduced, which recovers the existing concepts of strict feasibility for variational inequalities and complementarity problems. By using the equivalence characterization of nonemptiness and boundedness of the solution set for the generalized mixed variational inequality due to Zhong and Huang (J. Optim. Theory Appl. 147:454–472, 2010), it is proved that the generalized mixed variational inequality problem has a nonempty bounded solution set is equivalent to its strict feasibility.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9914-3
    DOI: 10.1007/s10957-011-9914-3
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    References listed on IDEAS

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    1. R. Hu & Y. P. Fang, 2009. "Feasibility-Solvability Theorem for a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 493-499, September.
    2. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    3. J. H. Fan & X. G. Wang, 2009. "Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 59-74, October.
    4. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
    5. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    6. 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.
    7. 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.
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    Cited by:

    1. 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.

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