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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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