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Inertial method for split null point problems with pseudomonotone variational inequality problems

  • *Corresponding author: Christian Chibueze Okeke

    *Corresponding author: Christian Chibueze Okeke 
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  • This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.

    Mathematics Subject Classification: Primary: 47H10; 49J20; Secondary: 49J40.


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  • Figure 1.  Example 5.1, Top Left: Case I; Top Right: Case II; Bottom: Case III

    Figure 2.  Example 5.2, Top Left: Case I; Top Right: Case II; Bottom: Case III

    Table 1.  Computational result for Example 5.1

    Case I Case II Case III
    Algo. 3.3 ($ \alpha =5 $) No of Iter. 7 8 8
    CPU time (sec) 0.034 0.0050 0.0034
    Algo. 3.3 ($ \alpha =3 $) No of Iter. 13 14 14
    CPU time (sec) 0.0109 0.0160 0.0076
    NUMA No of Iter. 51 54 58
    CPU time (sec) 0.0249 0.0296 0.0288
     | Show Table
    DownLoad: CSV

    Table 2.  Computational result for Example 5.2

    Case I Case II Case III
    Algo. 3.3 ($ \alpha =5 $) No of Iter. 8 16 90
    CPU time (sec) 0.0096 0.0223 0.0425
    Algo. 3.3 ($ \alpha =3 $) No of Iter. 8 19 323
    CPU time (sec) 0.0035 0.00089 0.4394
    NUMA No of Iter. 8 17 69
    CPU time (sec) 0.0051 0.0084 0.0257
     | Show Table
    DownLoad: CSV
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