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Nonemptiness and Compactness of Solution Sets to Weakly Homogeneous Generalized Variational Inequalities

Author

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  • Meng-Meng Zheng

    (Tianjin University)

  • Zheng-Hai Huang

    (Tianjin University)

  • Xue-Li Bai

    (South China Normal University)

Abstract

In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special variational inequalities and complementarity problems studied in recent years. By exploiting weakly homogeneous structures of involved map pairs and using degree theory, we establish a result which demonstrates the connection between weakly homogeneous generalized variational inequalities and weakly homogeneous generalized complementarity problems. Subsequently, we obtain a result on the nonemptiness and compactness of solution sets to weakly homogeneous generalized variational inequalities by utilizing Harker–Pang-type condition, which can lead to a Hartman–Stampacchia-type existence theorem. Last, we give several copositivity results for weakly homogeneous generalized variational inequalities, which can reduce to some existing ones.

Suggested Citation

  • Meng-Meng Zheng & Zheng-Hai Huang & Xue-Li Bai, 2021. "Nonemptiness and Compactness of Solution Sets to Weakly Homogeneous Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 919-937, June.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01866-3
    DOI: 10.1007/s10957-021-01866-3
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    References listed on IDEAS

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    1. Yong Wang & Zheng-Hai Huang & Liqun Qi, 2018. "Global Uniqueness and Solvability of Tensor Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 137-152, April.
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    5. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part I: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 1-23, October.
    6. M. Seetharama Gowda & Jong-Shi Pang, 1994. "Stability Analysis of Variational Inequalities and Nonlinear Complementarity Problems, via the Mixed Linear Complementarity Problem and Degree Theory," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 831-879, November.
    7. Zheng-Hai Huang & Liqun Qi, 2019. "Tensor Complementarity Problems—Part III: Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 771-791, December.
    8. Meng-Meng Zheng & Zheng-Hai Huang & Xiao-Xiao Ma, 2020. "Nonemptiness and Compactness of Solution Sets to Generalized Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 80-98, April.
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