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Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis

Author

Listed:
  • Shipra Singh

    (Technion -Israel Institute of Technology)

  • Savin Treanţă

    (University Politehnica of Bucharest)

Abstract

In this paper, the weak sharpness property of solution sets of a split variational inequality problem is studied. Further, finite convergence analysis of the iterative methods for solving the split variational inequality problem and its special case, split feasibility problem are investigated. We also provide an application of split variational inequality problem in traffic network analysis and numerically illustrate our derived results.

Suggested Citation

  • Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.
    • Handle: RePEc:spr:annopr:v:302:y:2021:i:1:d:10.1007_s10479-021-03971-y
    DOI: 10.1007/s10479-021-03971-y
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    References listed on IDEAS

    as
    1. Anurag Jayswal & Shipra Singh, 2018. "Characterization of weakly sharp solutions of a variational-type inequality with convex functional," Annals of Operations Research, Springer, vol. 269(1), pages 297-315, October.
    2. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    3. Li, J. & Huang, N.J. & Yang, X.Q., 2010. "Weak sharp minima for set-valued vector variational inequalities with an application," European Journal of Operational Research, Elsevier, vol. 205(2), pages 262-272, September.
    4. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    5. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    6. Lawphongpanich, Siriphong & Hearn, Donald W., 1984. "Simplical decomposition of the asymmetric traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 123-133, April.
    7. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    8. Wu, Zili, 2018. "Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping," European Journal of Operational Research, Elsevier, vol. 265(2), pages 448-453.
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