IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i3d10.1007_s10957-007-9279-9.html
   My bibliography  Save this article

Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem

Author

Listed:
  • J.-S. Chen

    (National Taiwan Normal University
    National Center for Theoretical Sciences)

Abstract

Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity, and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken the condition of strong monotonicity to the so-called uniform P *-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra. Moreover, we replace the monotonicity and strict feasibility by the so-called R 01 or R 02-functions to keep the property of bounded level sets.

Suggested Citation

  • J.-S. Chen, 2007. "Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 459-473, December.
  • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9279-9
    DOI: 10.1007/s10957-007-9279-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9279-9
    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/s10957-007-9279-9?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. Jein-Shan Chen, 2006. "Two classes of merit functions for the second-order cone complementarity problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 495-519, December.
    2. M. Seetharama Gowda & Roman Sznajder, 2006. "Automorphism Invariance of P - and GUS -Properties of Linear Transformations on Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 109-123, February.
    3. Yong-Jin Liu & Li-Wei Zhang & Yin-He Wang, 2006. "Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 473-495.
    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. Xin-He Miao & Yu-Lin Chang & Jein-Shan Chen, 2017. "On merit functions for p-order cone complementarity problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 155-173, May.
    2. Xin-He Miao & Shengjuan Guo & Nuo Qi & Jein-Shan Chen, 2016. "Constructions of complementarity functions and merit functions for circular cone complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 495-522, March.

    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. Lingchen Kong & Levent Tunçel & Naihua Xiu, 2012. "Existence and Uniqueness of Solutions for Homogeneous Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 357-376, May.
    2. Shaohua Pan & Jein-Shan Chen & Sangho Kum & Yongdo Lim, 2011. "The penalized Fischer-Burmeister SOC complementarity function," Computational Optimization and Applications, Springer, vol. 49(3), pages 457-491, July.
    3. J. Tao, 2010. "Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 575-596, March.
    4. S. H. Pan & J.-S. Chen, 2009. "Growth Behavior of Two Classes of Merit Functions for Symmetric Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 167-191, April.
    5. 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.
    6. Alberto Seeger & David Sossa, 2015. "Complementarity problems with respect to Loewnerian cones," Journal of Global Optimization, Springer, vol. 62(2), pages 299-318, June.
    7. Xin-He Miao & Yu-Lin Chang & Jein-Shan Chen, 2017. "On merit functions for p-order cone complementarity problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 155-173, May.
    8. Wang, Guoxin & Zhang, Jin & Zeng, Bo & Lin, Gui-Hua, 2018. "Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems," European Journal of Operational Research, Elsevier, vol. 265(2), pages 437-447.
    9. Yasushi Narushima & Nobuko Sagara & Hideho Ogasawara, 2011. "A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 79-101, April.
    10. S. H. Kum & Y. D. Lim, 2009. "Coercivity and Strong Semismoothness of the Penalized Fischer-Burmeister Function for the Symmetric Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 377-383, August.
    11. Roman Sznajder & M. Gowda & Melania Moldovan, 2012. "More results on Schur complements in Euclidean Jordan algebras," Journal of Global Optimization, Springer, vol. 53(1), pages 121-134, May.
    12. Michael Orlitzky, 2021. "Gaddum’s test for symmetric cones," Journal of Global Optimization, Springer, vol. 79(4), pages 927-940, April.
    13. Wei Hong Yang & Lei-Hong Zhang & Chungen Shen, 2017. "On the Range of the Pseudomonotone Second-Order Cone Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 504-522, May.
    14. J. Tao, 2009. "Positive Principal Minor Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 131-152, January.
    15. Roman Sznajder & M. Seetharama Gowda & Jiyuan Tao, 2012. "On the Uniform Nonsingularity Property for Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 306-319, May.
    16. J. Tao & I. Jeyaraman & G. Ravindran, 2016. "More results on column sufficiency property in Euclidean Jordan algebras," Annals of Operations Research, Springer, vol. 243(1), pages 229-243, August.
    17. Cong Cheng & Lianjie Tang, 2023. "A Smoothing Method for Sparse Programs by Symmetric Cone Constrained Generalized Equations," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    18. Linan Qu & Shujie Zhang & Hsiung-Cheng Lin & Ning Chen & Lingling Li, 2020. "Multiobjective Reactive Power Optimization of Renewable Energy Power Plants Based on Time-and-Space Grouping Method," Energies, MDPI, vol. 13(14), pages 1-15, July.
    19. Julio López & Rúben López & Héctor C. Ramírez, 2013. "Linear Complementarity Problems over Symmetric Cones: Characterization of Q b -transformations and Existence Results," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 741-768, December.
    20. Zijun Hao & Chieu Thanh Nguyen & Jein-Shan Chen, 2022. "An approximate lower order penalty approach for solving second-order cone linear complementarity problems," Journal of Global Optimization, Springer, vol. 83(4), pages 671-697, August.

    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:135:y:2007:i:3:d:10.1007_s10957-007-9279-9. 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.