IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v112y2002i1d10.1023_a1013048729944.html
   My bibliography  Save this article

Modified Goldstein–Levitin–Polyak Projection Method for Asymmetric Strongly Monotone Variational Inequalities

Author

Listed:
  • B. S. He

    (Nanjing University)

  • H. Yang

    (Hong Kong University of Science and Technology)

  • Q. Meng

    (Hong Kong University of Science and Technology)

  • D. R. Han

    (Nanjing University)

Abstract

In this paper, we present a modified Goldstein–Levitin–Polyak projection method for asymmetric strongly monotone variational inequality problems. A practical and robust stepsize choice strategy, termed self-adaptive procedure, is developed. The global convergence of the resulting algorithm is established under the same conditions used in the original projection method. Numerical results and comparison with some existing projection-type methods are given to illustrate the efficiency of the proposed method.

Suggested Citation

  • B. S. He & H. Yang & Q. Meng & D. R. Han, 2002. "Modified Goldstein–Levitin–Polyak Projection Method for Asymmetric Strongly Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 129-143, January.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:1:d:10.1023_a:1013048729944
    DOI: 10.1023/A:1013048729944
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1013048729944
    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:1013048729944?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. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    2. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    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. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    2. Min Zhang & Deren Han & Gang Qian & Xihong Yan, 2012. "A New Decomposition Method for Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 675-695, March.
    3. Chen, Anthony & Choi, Keechoo, 2017. "Solving the combined modal split and traffic assignment problem with two types of transit impedance functionAuthor-Name: Ryu, Seungkyu," European Journal of Operational Research, Elsevier, vol. 257(3), pages 870-880.
    4. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X. & Wu, Ting, 2009. "Self-adaptive projection method for co-coercive variational inequalities," European Journal of Operational Research, Elsevier, vol. 196(1), pages 43-48, July.
    5. Liu, Zhiyuan & Chen, Xinyuan & Meng, Qiang & Kim, Inhi, 2018. "Remote park-and-ride network equilibrium model and its applications," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 37-62.
    6. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.

    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. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    2. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    3. Zhang, J. & Meng, M. & Wang, David, Z.W., 2019. "A dynamic pricing scheme with negative prices in dockless bike sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 201-224.
    4. Zhang, Ding & Nagurney, Anna & Wu, Jiahao, 2001. "On the equivalence between stationary link flow patterns and traffic network equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 731-748, September.
    5. Y. W. Xu & J. H. Wu & M. Florian & P. Marcotte & D. L. Zhu, 1999. "Advances in the Continuous Dynamic Network Loading Problem," Transportation Science, INFORMS, vol. 33(4), pages 341-353, November.
    6. Wang, Dong & Liao, Feixiong, 2023. "Incentivized user-based relocation strategies for moderating supply–demand dynamics in one-way car-sharing services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    7. Anna Nagurney & Dong Li, 2015. "A supply chain network game theory model with product differentiation, outsourcing of production and distribution, and quality and price competition," Annals of Operations Research, Springer, vol. 226(1), pages 479-503, March.
    8. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    9. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    10. Cojocaru, Monica-Gabriela & Daniele, Patrizia & Nagurney, Anna, 2006. "Double-layered dynamics: A unified theory of projected dynamical systems and evolutionary variational inequalities," European Journal of Operational Research, Elsevier, vol. 175(1), pages 494-507, November.
    11. Xing Gao & Weijun Zhong & Shue Mei, 2013. "Stochastic Evolutionary Game Dynamics and Their Selection Mechanisms," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 233-247, February.
    12. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    13. Ziyou Gao & Yunchao Qu & Xingang Li & Jiancheng Long & Hai-Jun Huang, 2014. "Simulating the Dynamic Escape Process in Large Public Places," Operations Research, INFORMS, vol. 62(6), pages 1344-1357, December.
    14. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    15. Nagurney, Anna & Dong, June, 2002. "A multiclass, multicriteria traffic network equilibrium model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 445-469, June.
    16. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.
    17. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    18. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    19. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    20. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.

    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:112:y:2002:i:1:d:10.1023_a:1013048729944. 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.