IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i4d10.1007_s10898-021-01040-z.html
   My bibliography  Save this article

Unique solvability of weakly homogeneous generalized variational inequalities

Author

Listed:
  • Xueli Bai

    (South China Normal University)

  • Mengmeng Zheng

    (Tianjin University)

  • Zheng-Hai Huang

    (Tianjin University)

Abstract

An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper focuses on studying the uniqueness and solvability of the generalized variational inequality with a pair of weakly homogeneous mappings. By using a weaker condition than the strong monotonicity and some additional conditions, we achieve several results on the unique solvability to the underlying problem, which are exported by making use of the exceptional family of elements. As an adjunct, we also obtain the nonemptiness and compactness of the solution sets to the weakly homogeneous generalized variational inequality under some appropriate conditions. The conclusions presented in this paper are new or supplements to the existing ones even when the problem comes down to its important subclasses studied in recent years.

Suggested Citation

  • Xueli Bai & Mengmeng Zheng & Zheng-Hai Huang, 2021. "Unique solvability of weakly homogeneous generalized variational inequalities," Journal of Global Optimization, Springer, vol. 80(4), pages 921-943, August.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:4:d:10.1007_s10898-021-01040-z
    DOI: 10.1007/s10898-021-01040-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-021-01040-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-021-01040-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. M. Seetharama Gowda, 1993. "Applications of Degree Theory to Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 868-879, November.
    3. Vu Trung Hieu, 2020. "Solution maps of polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 77(4), pages 807-824, August.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    5. J. Han & Z. H. Huang & S. C. Fang, 2004. "Solvability of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 501-520, September.
    6. Xue-Li Bai & Zheng-Hai Huang & Yong Wang, 2016. "Global Uniqueness and Solvability for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 72-84, July.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Tong-tong Shang & Guo-ji Tang, 2023. "Mixed polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 86(4), pages 953-988, August.
    3. Tong-tong Shang & Jing Yang & Guo-ji Tang, 2022. "Generalized Polynomial Complementarity Problems over a Polyhedral Cone," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 443-483, February.
    4. Xue-Li Bai & Zheng-Hai Huang & Xia Li, 2019. "Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-19, April.
    5. Vu Trung Hieu, 2020. "Solution maps of polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 77(4), pages 807-824, August.
    6. 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.
    7. 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.
    8. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
    9. Yan, Weijie & Ling, Chen & Ling, Liyun & He, Hongjin, 2019. "Generalized tensor equations with leading structured tensors," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 311-324.
    10. Tong-tong Shang & Guo-ji Tang, 2023. "Structured tensor tuples to polynomial complementarity problems," Journal of Global Optimization, Springer, vol. 86(4), pages 867-883, August.
    11. Punit Kumar Yadav & Palpandi Karuppaiah, 2023. "Generalizations of $$R_0$$ R 0 and $$\textbf{SSM}$$ SSM Properties for Extended Horizontal Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 392-414, October.
    12. Ping-Fan Dai & Shi-Liang Wu, 2022. "The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 976-1006, December.
    13. K. Palpandi & Sonali Sharma, 2021. "Tensor Complementarity Problems with Finite Solution Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 951-965, September.
    14. M. Seetharama Gowda, 2019. "Weighted LCPs and interior point systems for copositive linear transformations on Euclidean Jordan algebras," Journal of Global Optimization, Springer, vol. 74(2), pages 285-295, June.
    15. Shouqiang Du & Weiyang Ding & Yimin Wei, 2021. "Acceptable Solutions and Backward Errors for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 260-276, January.
    16. Vu Trung Hieu, 2019. "On the R0-Tensors and the Solution Map of Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 163-183, April.
    17. Xuezhong Wang & Maolin Che & Yimin Wei, 2022. "Randomized Kaczmarz methods for tensor complementarity problems," Computational Optimization and Applications, Springer, vol. 82(3), pages 595-615, July.
    18. 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.
    19. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2020. "On ill-posedness and stability of tensor variational inequalities: application to an economic equilibrium," Journal of Global Optimization, Springer, vol. 77(1), pages 125-141, May.
    20. Xiaoni Chi & M. Seetharama Gowda & Jiyuan Tao, 2019. "The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra," Journal of Global Optimization, Springer, vol. 73(1), pages 153-169, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:80:y:2021:i:4:d:10.1007_s10898-021-01040-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.