IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v54y2013i1p45-64.html
   My bibliography  Save this article

Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization

Author

Listed:
  • Gonglin Yuan
  • Zengxin Wei
  • Zhongxing Wang

Abstract

By means of a gradient strategy, the Moreau-Yosida regularization, limited memory BFGS update, and proximal method, we propose a trust-region method for nonsmooth convex minimization. The search direction is the combination of the gradient direction and the trust-region direction. The global convergence of this method is established under suitable conditions. Numerical results show that this method is competitive to other two methods. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:45-64
    DOI: 10.1007/s10589-012-9485-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-012-9485-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-012-9485-8?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. Liqun Qi, 1999. "Regular Pseudo-Smooth NCP and BVIP Functions and Globally and Quadratically Convergent Generalized Newton Methods for Complementarity and Variational Inequality Problems," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 440-471, May.
    2. J. R. Birge & L. Qi & Z. Wei, 1998. "Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 357-383, May.
    3. Ju-liang Zhang & Yong Wang, 2003. "A new trust region method for nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 283-298, November.
    4. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    5. L. Qi & X. J. Tong & D. H. Li, 2004. "Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 601-625, March.
    6. Yunhai Xiao & Dong-Hui Li, 2008. "An active set limited memory BFGS algorithm for large-scale bound constrained optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 443-454, June.
    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. Yong Li & Gonglin Yuan & Zhou Sheng, 2018. "An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-16, January.
    2. Tsegay Giday Woldu & Haibin Zhang & Xin Zhang & Yemane Hailu Fissuh, 2020. "A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 223-238, April.
    3. Qi Tian & Xiaoliang Wang & Liping Pang & Mingkun Zhang & Fanyun Meng, 2021. "A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    4. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    5. Zengru Cui & Gonglin Yuan & Zhou Sheng & Wenjie Liu & Xiaoliang Wang & Xiabin Duan, 2015. "A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-15, October.
    6. Zhou Sheng & Gonglin Yuan, 2018. "An effective adaptive trust region algorithm for nonsmooth minimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 251-271, September.

    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. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. J. Chen & L. Qi, 2010. "Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 223-242, November.
    3. L. Qi & X. J. Tong & D. H. Li, 2004. "Active-Set Projected Trust-Region Algorithm for Box-Constrained Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 601-625, March.
    4. Sha Lu & Zengxin Wei & Lue Li, 2012. "A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 51(2), pages 551-573, March.
    5. Dong-Hui Li & Liqun Qi & Judy Tam & Soon-Yi Wu, 2004. "A Smoothing Newton Method for Semi-Infinite Programming," Journal of Global Optimization, Springer, vol. 30(2), pages 169-194, November.
    6. Tsegay Giday Woldu & Haibin Zhang & Xin Zhang & Yemane Hailu Fissuh, 2020. "A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 223-238, April.
    7. John Duggan & Tasos Kalandrakis, 2011. "A Newton collocation method for solving dynamic bargaining games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(3), pages 611-650, April.
    8. H. Xu & B. M. Glover, 1997. "New Version of the Newton Method for Nonsmooth Equations," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 395-415, May.
    9. Sanja Rapajić & Zoltan Papp, 2017. "A nonmonotone Jacobian smoothing inexact Newton method for NCP," Computational Optimization and Applications, Springer, vol. 66(3), pages 507-532, April.
    10. 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.
    11. C. Kanzow & H. Qi & L. Qi, 2003. "On the Minimum Norm Solution of Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 333-345, February.
    12. Kenji Ueda & Nobuo Yamashita, 2012. "Global Complexity Bound Analysis of the Levenberg–Marquardt Method for Nonsmooth Equations and Its Application to the Nonlinear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 450-467, February.
    13. Y. D. Chen & Y. Gao & Y.-J. Liu, 2010. "An Inexact SQP Newton Method for Convex SC1 Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 33-49, July.
    14. Y. Gao, 2004. "Representation of the Clarke Generalized Jacobian via the Quasidifferential," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 519-532, December.
    15. Alain B. Zemkoho & Shenglong Zhou, 2021. "Theoretical and numerical comparison of the Karush–Kuhn–Tucker and value function reformulations in bilevel optimization," Computational Optimization and Applications, Springer, vol. 78(2), pages 625-674, March.
    16. 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.
    17. Kalandrakis, Tasos, 2015. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Games and Economic Behavior, Elsevier, vol. 94(C), pages 29-38.
    18. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
    19. Gonglin Yuan & Zhou Sheng & Wenjie Liu, 2016. "The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    20. Gerdts, Matthias, 2008. "A nonsmooth Newton’s method for control-state constrained optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 925-936.

    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:coopap:v:54:y:2013:i:1:p:45-64. 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.