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Self-adaptive projection method for co-coercive variational inequalities

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  • He, Bingsheng
  • He, Xiao-Zheng
  • Liu, Henry X.
  • Wu, Ting

Abstract

In some real-world problems, the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables. In this case, if the mapping is co-coercive, the basic projection method is applicable. However, in order to determine the step size, the existing basic projection method needs to know the co-coercive modulus in advance. In practice, usually even if the mapping can be characterized co-coercive, it is difficult to evaluate the modulus, and a conservative estimation will lead an extremely slow convergence. In view of this point, this paper presents a self-adaptive projection method without knowing the co-coercive modulus. We also give a real-life example to demonstrate the practicability of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:1:p:43-48
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    References listed on IDEAS

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    1. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
    2. Nagurney, Anna, 1986. "An algorithm for the single commodity spatial price equilibrium problem," Regional Science and Urban Economics, Elsevier, vol. 16(4), pages 573-588, November.
    3. 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.
    4. Stella Dafermos & Anna Nagurney, 1989. "Supply and Demand Equilibration Algorithms for a Class of Market Equilibrium Problems," Transportation Science, INFORMS, vol. 23(2), pages 118-124, May.
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    Cited by:

    1. He, Xiaozheng & Liu, Henry X., 2011. "Inverse variational inequalities with projection-based solution methods," European Journal of Operational Research, Elsevier, vol. 208(1), pages 12-18, January.
    2. Ma, Jie & Xu, Min & Meng, Qiang & Cheng, Lin, 2020. "Ridesharing user equilibrium problem under OD-based surge pricing strategy," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 1-24.
    3. Wang, Hua & Meng, Qiang & Zhang, Xiaoning, 2020. "Multiple equilibrium behaviors of auto travellers and a freight carrier under the cordon-based large-truck restriction regulation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    4. Giuseppe Marino & Hong-Kun Xu, 2011. "Explicit Hierarchical Fixed Point Approach to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 61-78, April.

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