IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v93y2025i2d10.1007_s10898-024-01392-2.html

The projected-type method for the extended vertical linear complementarity problem revisited

Author

Listed:
  • Cui-Xia Li

    (Yunnan Normal University)

  • Shi-Liang Wu

    (Yunnan Normal University
    Yunnan Normal University)

Abstract

In this paper, we further study the projected-type method for the extended vertical linear complementarity problem. By making use of some basic absolute value inequalities, some new convergence properties of the projected-type method are obtained. Compared with the existing results in the literature, the convergence range of the projected-type method is enlarged. By several numerical experiments, we also show the performance of the projected-type method.

Suggested Citation

  • Cui-Xia Li & Shi-Liang Wu, 2025. "The projected-type method for the extended vertical linear complementarity problem revisited," Journal of Global Optimization, Springer, vol. 93(2), pages 535-550, October.
    • Handle: RePEc:spr:jglopt:v:93:y:2025:i:2:d:10.1007_s10898-024-01392-2
    DOI: 10.1007/s10898-024-01392-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-024-01392-2
    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/s10898-024-01392-2?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Francesco Mezzadri & Emanuele Galligani, 2022. "Projected Splitting Methods for Vertical Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 598-620, June.
    2. Gowda, M Seetharama & Sznajder, Roman, 1996. "A Generalization of the Nash Equilibrium Theorem on Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 1-12.
    3. 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.
    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. Cui-Xia Li & Shi-Liang Wu, 2026. "Vertical Linear Complementarity Problem Via the New Modulus-Based Matrix Splitting Method," Journal of Optimization Theory and Applications, Springer, vol. 208(3), pages 1-23, March.
    2. Ting Zhang & Yong Wang & Zheng-Hai Huang, 2024. "Projected fixed-point method for vertical tensor complementarity problems," Computational Optimization and Applications, Springer, vol. 89(1), pages 219-245, September.
    3. Dipti Dubey & S. K. Neogy & Debasish Ghorui, 2017. "Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 535-554, December.
    4. Xue-liu Li & Yi-rong Jiang & Yuning Yang & Guo-ji Tang, 2025. "Extended vertical tensor complementarity problems with finite solution sets," Journal of Global Optimization, Springer, vol. 92(2), pages 431-452, June.
    5. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    6. Bhaskar Ray Chaudhury & Jugal Garg & Peter McGlaughlin & Ruta Mehta, 2023. "A Complementary Pivot Algorithm for Competitive Allocation of a Mixed Manna," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1630-1656, August.
    7. Karan N. Chadha & Ankur A. Kulkarni, 2022. "On independent cliques and linear complementarity problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1036-1057, December.
    8. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    9. Parthasarathy T & Ravindran G & Sunil Kumar, 2025. "On Q-tensors," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-13, November.
    10. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    11. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    12. Guo-qiang Wang & Yu-jing Yue & Xin-zhong Cai, 2009. "Weighted-path-following interior-point algorithm to monotone mixed linear complementarity problem," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 435-445, December.
    13. 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.
    14. G. L. Zhou & L. Caccetta, 2008. "Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 379-392, November.
    15. A. K. Das, 2016. "Properties of some matrix classes based on principal pivot transform," Annals of Operations Research, Springer, vol. 243(1), pages 375-382, August.
    16. Xi-Ming Fang & Zhi-Jun Qiao & Heng-Jun Zhao, 2019. "The Block Principal Pivoting Algorithm for the Linear Complementarity Problem with an M‐Matrix," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    17. Meijuan Shang & Chao Zhang & Naihua Xiu, 2014. "Minimal Zero Norm Solutions of Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 795-814, December.
    18. Massol, Olivier & Rifaat, Omer, 2018. "Phasing out the U.S. Federal Helium Reserve: Policy insights from a world helium model," Resource and Energy Economics, Elsevier, vol. 54(C), pages 186-211.
    19. S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    20. Diethard Klatte, 2026. "Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping," Computational Management Science, Springer, vol. 23(1), pages 1-25, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:93:y:2025:i:2:d:10.1007_s10898-024-01392-2. 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.