IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v111y2001i2d10.1023_a1011942620208.html
   My bibliography  Save this article

Inexact Implicit Method with Variable Parameter for Mixed Monotone Variational Inequalities

Author

Listed:
  • S. L. Wang

    (Nanjing University)

  • H. Yang

    (Hong Kong University of Science and Technology)

  • B. S. He

    (Nanjing University)

Abstract

In this paper, we focus on a useful modification of the implicit method by Noor (Ref. 1) for mixed variational inequalities. Experience on applications has shown that the number of iterations of the original method depends significantly on the penalty parameter. One of the contributions of the proposed method is that we allow the penalty parameter to be variable. By introducing a self-adaptive rule, we find that our method is more flexible and efficient than the original one. Another contribution is that we require only an inexact solution of the nonlinear equations at each iteration. A detailed convergence analysis of our method is also included.

Suggested Citation

  • S. L. Wang & H. Yang & B. S. He, 2001. "Inexact Implicit Method with Variable Parameter for Mixed Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 431-443, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011942620208
    DOI: 10.1023/A:1011942620208
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1011942620208
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1011942620208?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. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    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. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    2. Lu-Chuan Zeng & Jen-Chih Yao, 2005. "Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 211-224, November.

    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. Zhao, Baining & Qian, Tong & Li, Weiwei & Xin, Yanli & Zhao, Wei & Lin, Zekang & Tang, Wenhu & Jin, Xin & Cao, Wangzhang & Pan, Tingzhe, 2024. "Fast distributed co-optimization of electricity and natural gas systems hedging against wind fluctuation and uncertainty," Energy, Elsevier, vol. 298(C).
    2. Kun Jin & Yevgeniy Vorobeychik & Mingyan Liu, 2021. "Multi-Scale Games: Representing and Solving Games on Networks with Group Structure," Papers 2101.08314, arXiv.org.
    3. Myungjin Kim & Li Wang & Yuyu Zhou, 2021. "Spatially Varying Coefficient Models with Sign Preservation of the Coefficient Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 367-386, September.
    4. Dolgopolik, Maksim V., 2021. "The alternating direction method of multipliers for finding the distance between ellipsoids," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. Yao, Yu & Zhu, Xiaoning & Dong, Hongyu & Wu, Shengnan & Wu, Hailong & Carol Tong, Lu & Zhou, Xuesong, 2019. "ADMM-based problem decomposition scheme for vehicle routing problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 156-174.
    6. Bingsheng He & Feng Ma & Xiaoming Yuan, 2020. "Optimally linearizing the alternating direction method of multipliers for convex programming," Computational Optimization and Applications, Springer, vol. 75(2), pages 361-388, March.
    7. Lijun Xu & Bo Yu & Yin Zhang, 2017. "An alternating direction and projection algorithm for structure-enforced matrix factorization," Computational Optimization and Applications, Springer, vol. 68(2), pages 333-362, November.
    8. Zheng Peng & Wenxing Zhu, 2013. "An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 533-551, May.
    9. Hou, Yanqiu & Bao, Minglei & Sang, Maosheng & Ding, Yi, 2024. "A market framework to exploit the multi-energy operating reserve of smart energy hubs in the integrated electricity-gas systems," Applied Energy, Elsevier, vol. 357(C).
    10. Liu, Zhiyuan & Zhang, Honggang & Zhang, Kai & Zhou, Zihan, 2023. "Integrating alternating direction method of multipliers and bush for solving the traffic assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    11. S. L. Wang & L. Z. Liao, 2001. "Decomposition Method with a Variable Parameter for a Class of Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 415-429, May.
    12. Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    13. Bin Gao & Feng Ma, 2018. "Symmetric Alternating Direction Method with Indefinite Proximal Regularization for Linearly Constrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 178-204, January.
    14. Giorgio Costa & Roy H. Kwon, 2020. "Generalized risk parity portfolio optimization: an ADMM approach," Journal of Global Optimization, Springer, vol. 78(1), pages 207-238, September.
    15. Dirk A. Lorenz & Quoc Tran-Dinh, 2019. "Non-stationary Douglas–Rachford and alternating direction method of multipliers: adaptive step-sizes and convergence," Computational Optimization and Applications, Springer, vol. 74(1), pages 67-92, September.
    16. Tan, Jin & Wu, Qiuwei & Wei, Wei & Liu, Feng & Li, Canbing & Zhou, Bin, 2020. "Decentralized robust energy and reserve Co-optimization for multiple integrated electricity and heating systems," Energy, Elsevier, vol. 205(C).
    17. Yunhai Xiao & Hong Zhu & Soon-Yi Wu, 2013. "Primal and dual alternating direction algorithms for ℓ 1 -ℓ 1 -norm minimization problems in compressive sensing," Computational Optimization and Applications, Springer, vol. 54(2), pages 441-459, March.
    18. Sharifian, Yeganeh & Abdi, Hamdi, 2024. "Multi-area economic dispatch problem: Methods, uncertainties, and future directions," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    19. Wu, Yiqian & Zhang, Xuan & Sun, Hongbin, 2021. "A multi-time-scale autonomous energy trading framework within distribution networks based on blockchain," Applied Energy, Elsevier, vol. 287(C).
    20. X. Wang & S. Li & X. Kou & Q. Zhang, 2015. "A new alternating direction method for linearly constrained nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 695-709, 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:111:y:2001:i:2:d:10.1023_a:1011942620208. 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.