IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v99y1998i2d10.1023_a1021786630040.html
   My bibliography  Save this article

Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems

Author

Listed:
  • J. H. Wu

    (Université de Montréal)

Abstract

In this paper, we present a long-step primal path-following algorithm and prove its global convergence under usual assumptions. It is seen that the short-step algorithm is a special case of the long-step algorithm for a specific selection of the parameters and the initial solution. Our theoretical result indicates that the long-step algorithm is more flexible. Numerical results indicate that the long-step algorithm converges faster than the short-step algorithm.

Suggested Citation

  • J. H. Wu, 1998. "Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 509-531, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021786630040
    DOI: 10.1023/A:1021786630040
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021786630040
    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:1021786630040?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. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    2. K. O. Kortanek & Jishan Zhu, 1993. "A Polynomial Barrier Algorithm for Linearly Constrained Convex Programming Problems," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 116-127, February.
    3. Jong-Shi Pang, 1990. "Newton's Method for B-Differentiable Equations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 311-341, 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. G. Salmon & V. H. Nguyen & J. J. Strodiot, 2000. "Coupling the Auxiliary Problem Principle and Epiconvergence Theory to Solve General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 629-657, March.
    2. T. T. Hue & J. J. Strodiot & V. H. Nguyen, 2004. "Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 119-145, April.

    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. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    2. Anna Nagurney & Qiang Qiang, 2008. "An efficiency measure for dynamic networks modeled as evolutionary variational inequalities with application to the Internet and vulnerability analysis," Netnomics, Springer, vol. 9(1), pages 1-20, January.
    3. Ahipaşaoğlu, Selin Damla & Meskarian, Rudabeh & Magnanti, Thomas L. & Natarajan, Karthik, 2015. "Beyond normality: A cross moment-stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 333-354.
    4. Ran, Bin & Hall, Randolph & Boyce, David E., 1995. "A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt84t190b3, Institute of Transportation Studies, UC Berkeley.
    5. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    6. Younes Hamdouch & Siriphong Lawphongpanich, 2010. "Congestion Pricing for Schedule-Based Transit Networks," Transportation Science, INFORMS, vol. 44(3), pages 350-366, August.
    7. 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.
    8. Xiaoming Yuan, 2011. "An improved proximal alternating direction method for monotone variational inequalities with separable structure," Computational Optimization and Applications, Springer, vol. 49(1), pages 17-29, May.
    9. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    10. V. Ruggiero & L. Zanni, 2000. "A Modified Projection Algorithm for Large Strictly-Convex Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 255-279, February.
    11. Ennio Cascetta & Mariano Gallo & Bruno Montella, 2006. "Models and algorithms for the optimization of signal settings on urban networks with stochastic assignment models," Annals of Operations Research, Springer, vol. 144(1), pages 301-328, April.
    12. A. de Palma & Y. Nesterov, 2001. "Stationary Dynamic Solutions in Congested Transportation Networks: Summary and Perspectives," THEMA Working Papers 2001-19, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Verhoef, Erik T., 2002. "Second-best congestion pricing in general static transportation networks with elastic demands," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 281-310, May.
    14. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    15. 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.
    16. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2020. "Static traffic assignment with residual queues and spillback," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 303-319.
    17. Sang Nguyen & Stefano Pallottino & Federico Malucelli, 2001. "A Modeling Framework for Passenger Assignment on a Transport Network with Timetables," Transportation Science, INFORMS, vol. 35(3), pages 238-249, August.
    18. Y. B. Zhao, 1999. "Extended Projection Methods for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 219-231, January.
    19. D E Boyce, 1984. "Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects," Environment and Planning A, , vol. 16(11), pages 1445-1474, November.
    20. I. Konnov, 2015. "On auction equilibrium models with network applications," Netnomics, Springer, vol. 16(1), pages 107-125, 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:99:y:1998:i:2:d:10.1023_a:1021786630040. 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.