IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v183y2019i3d10.1007_s10957-019-01573-0.html
   My bibliography  Save this article

Tensor Complementarity Problems—Part III: Applications

Author

Listed:
  • Zheng-Hai Huang

    (Tianjin University)

  • Liqun Qi

    (Hangzhou Dianzi University
    The Hong Kong Polytechnic University)

Abstract

We have reviewed some theoretical and algorithmic developments for tensor complementarity problems and related models in the first part and the second part of this paper, respectively. In this part, we present a survey for some applications of tensor complementarity problems and polynomial complementarity problems. We first describe some equivalent classes of tensor complementarity problems and polynomial complementarity problems, since many practical problems can be modeled as forms of those equivalent problems; and then, we review three practical applications of tensor complementarity problems and polynomial complementarity problems. The first practical application is about a class of multi-person noncooperative games, which is modeled as a tensor complementarity problem, and particularly, an explicit relationship between the solutions to these two classes of problems is presented. The second practical problem is about the hypergraph clustering problem, which can be solved by a tensor complementarity problem. The third practical problem is about a class of traffic equilibrium problems, which is modeled as a polynomial complementarity problem. Some further issues are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:3:d:10.1007_s10957-019-01573-0
    DOI: 10.1007/s10957-019-01573-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01573-0
    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/s10957-019-01573-0?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. Haibin Chen & Zheng-Hai Huang & Liqun Qi, 2017. "Copositivity Detection of Tensors: Theory and Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 746-761, September.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. 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.
    4. Haibin Chen & Zheng-Hai Huang & Liqun Qi, 2018. "Copositive tensor detection and its applications in physics and hypergraphs," Computational Optimization and Applications, Springer, vol. 69(1), pages 133-158, January.
    5. Shouqiang Du & Liping Zhang, 2019. "A mixed integer programming approach to the tensor complementarity problem," Journal of Global Optimization, Springer, vol. 73(4), pages 789-800, April.
    6. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Shouqiang Du & Maolin Che & Yimin Wei, 2020. "Stochastic structured tensors to stochastic complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 649-668, April.
    3. Lu-Bin Cui & Yu-Dong Fan & Yi-Sheng Song & Shi-Liang Wu, 2022. "The Existence and Uniqueness of Solution for Tensor Complementarity Problem and Related Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 321-334, January.
    4. 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.
    5. Zhenyu Ming & Liping Zhang & Liqun Qi, 2020. "Expected residual minimization method for monotone stochastic tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 77(3), pages 871-896, December.
    6. Yang Xu & Guyan Ni & Mengshi Zhang, 2024. "Bounds of the Solution Set to the Polynomial Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 146-164, October.
    7. 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.
    8. Hong-Bo Guan & Dong-Hui Li, 2020. "Linearized Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 972-987, March.
    9. 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.
    10. Lulu Cheng & Xinzhen Zhang, 2020. "A semidefinite relaxation method for second-order cone polynomial complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 629-647, April.
    11. Vu Trung Hieu & Yimin Wei & Jen-Chih Yao, 2020. "Notes on the Optimization Problems Corresponding to Polynomial Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 687-695, February.
    12. 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.
    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. 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.
    15. 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.
    16. Shouqiang Du & Liyuan Cui & Yuanyuan Chen & Yimin Wei, 2022. "Stochastic Tensor Complementarity Problem with Discrete Distribution," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 912-929, March.
    17. 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.
    18. Xuezhong Wang & Ping Wei & Yimin Wei, 2023. "A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 334-357, April.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yisheng Song & Xudong Li, 2022. "Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 334-346, October.
    6. 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.
    7. 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.
    8. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.
    9. 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.
    10. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    11. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.
    12. 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.
    13. Liqun Qi & Zheng-Hai Huang, 2019. "Tensor Complementarity Problems—Part II: Solution Methods," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 365-385, November.
    14. Haibin Chen & Zheng-Hai Huang & Liqun Qi, 2018. "Copositive tensor detection and its applications in physics and hypergraphs," Computational Optimization and Applications, Springer, vol. 69(1), pages 133-158, January.
    15. 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.
    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. Christian Bidard, 2010. "Complementarity Problems and General Equilibrium," Working Papers hal-04140923, HAL.
    18. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Solving Discrete Zero Point Problems with Vector Labeling," Other publications TiSEM 9bd940ee-3fe6-4201-aede-7, Tilburg University, School of Economics and Management.
    19. Ya-nan Zheng & Wei Wu, 2018. "On a Class of Semi-Positive Tensors in Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 127-136, April.
    20. Shouqiang Du & Maolin Che & Yimin Wei, 2020. "Stochastic structured tensors to stochastic complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 649-668, April.

    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:joptap:v:183:y:2019:i:3:d:10.1007_s10957-019-01573-0. 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.