IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v269y2015icp155-168.html
   My bibliography  Save this article

A generalized Newton method for absolute value equations associated with circular cones

Author

Listed:
  • Miao, Xin-He
  • Yang, Jiantao
  • Hu, Shenglong

Abstract

In this paper, we study a class of absolute value equations associated with circular cone (CCAVE for short), which is a generalization of the absolute value equations discussed recently in the literature, analogously to the fact that circular cone is the very generalization of the second-order cone. We show that the CCAVE is equivalent to a class of circular cone linear complementarity problems, and hence generalize the well-known equivalence between absolute value equations and linear complementarity problems. Useful properties of the generalized differential of the absolute value function over the circular cone are investigated, which helps to propose a generalized Newton method for solving the CCAVE. The convergence of this method is established under mild conditions, as well as the efficiency of which is illustrated by some preliminary numerical results.

Suggested Citation

  • Miao, Xin-He & Yang, Jiantao & Hu, Shenglong, 2015. "A generalized Newton method for absolute value equations associated with circular cones," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 155-168.
  • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:155-168
    DOI: 10.1016/j.amc.2015.07.064
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315009832
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.07.064?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. Zheng-Hai Huang & Tie Ni, 2010. "Smoothing algorithms for complementarity problems over symmetric cones," Computational Optimization and Applications, Springer, vol. 45(3), pages 557-579, April.
    2. C. Zhang & Q. J. Wei, 2009. "Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 391-403, November.
    3. Olvi L. Mangasarian, 2014. "Absolute Value Equation Solution Via Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 870-876, June.
    4. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    5. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
    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. Shota Yamanaka & Nobuo Yamashita, 2018. "Duality of nonconvex optimization with positively homogeneous functions," Computational Optimization and Applications, Springer, vol. 71(2), pages 435-456, November.
    2. Jingyong Tang & Jinchuan Zhou, 2020. "Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones," Annals of Operations Research, Springer, vol. 295(2), pages 787-808, December.

    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. J. Y. Bello Cruz & O. P. Ferreira & L. F. Prudente, 2016. "On the global convergence of the inexact semi-smooth Newton method for absolute value equation," Computational Optimization and Applications, Springer, vol. 65(1), pages 93-108, September.
    2. Shota Yamanaka & Nobuo Yamashita, 2018. "Duality of nonconvex optimization with positively homogeneous functions," Computational Optimization and Applications, Springer, vol. 71(2), pages 435-456, November.
    3. An Wang & Yang Cao & Jing-Xian Chen, 2019. "Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 216-230, April.
    4. Zhang, Jian-Jun, 2015. "The relaxed nonlinear PHSS-like iteration method for absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 266-274.
    5. Milan Hladík, 2018. "Bounds for the solutions of absolute value equations," Computational Optimization and Applications, Springer, vol. 69(1), pages 243-266, January.
    6. Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
    7. Shi-Liang Wu & Peng Guo, 2016. "On the Unique Solvability of the Absolute Value Equation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 705-712, May.
    8. Cuixia Li, 2022. "Sufficient Conditions for the Unique Solution of a New Class of Sylvester-Like Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 676-683, November.
    9. Moosaei, H. & Ketabchi, S. & Noor, M.A. & Iqbal, J. & Hooshyarbakhsh, V., 2015. "Some techniques for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 696-705.
    10. Li Fangping & Yang Yuguo & Wu Yue, 2016. "The Optimization of Reservoir Based on the Combination of ABC Classification Method and Linear Programming Method," International Journal of Business and Management, Canadian Center of Science and Education, vol. 11(11), pages 156-156, October.
    11. Jingyong Tang & Hongchao Zhang, 2021. "A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 679-715, June.
    12. Olvi L. Mangasarian, 2014. "Absolute Value Equation Solution Via Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 870-876, June.
    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. Li, Yuan-Min & Wei, Deyun, 2015. "A generalized smoothing Newton method for the symmetric cone complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 335-345.
    15. Tang, Jingyong & Zhou, Jinchuan & Fang, Liang, 2015. "A non-monotone regularization Newton method for the second-order cone complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 743-756.
    16. Xiangjing Liu & Sanyang Liu, 2020. "A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 229-247, October.
    17. Jingyong Tang & Jinchuan Zhou, 2020. "Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones," Annals of Operations Research, Springer, vol. 295(2), pages 787-808, December.
    18. Nan Lu & Zheng-Hai Huang, 2014. "A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 446-464, May.
    19. L. Abdallah & M. Haddou & T. Migot, 2019. "A sub-additive DC approach to the complementarity problem," Computational Optimization and Applications, Springer, vol. 73(2), pages 509-534, June.
    20. Jingyong Tang & Jinchuan Zhou & Hongchao Zhang, 2023. "An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 641-665, February.

    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:eee:apmaco:v:269:y:2015:i:c:p:155-168. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.