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On a modified extragradient method for variational inequality problem with application to industrial electricity production

  • * Corresponding author: Yekini Shehu

    * Corresponding author: Yekini Shehu 
Abstract Full Text(HTML) Figure(7) / Table(3) Related Papers Cited by
  • In this paper, we present a modified extragradient-type method for solving the variational inequality problem involving uniformly continuous pseudomonotone operator. It is shown that under certain mild assumptions, this method is strongly convergent in infinite dimensional real Hilbert spaces. We give some numerical computational experiments which involve a comparison of our proposed method with other existing method in a model on industrial electricity production.

    Mathematics Subject Classification: Primary: 47H06, 47H09, 47J05; Secondary: 47J25.

    Citation:

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  • Figure 3.  Algorithm (5.2) with $\rho=0.3$

    Figure 6.  Algorithm (5.2) with $\rho=0.8$

    Figure 9.  Algorithm (5.2) with $\rho=1.2$

    Figure 12.  Algorithm (5.2) with $\rho=1.6$

    Figure 13.  Algorithm (5.3) Case Ⅰ

    Figure 14.  Algorithm (5.3) Case Ⅱ

    Figure 15.  Algorithm (5.3) Case Ⅲ

    Table 2.  Algorithm (5.2) with different values of $\rho$

    No. of Iterations CPU (Time)
    $\rho = 0.3$ 5 0.0163
    $\rho = 0.8$ 10 0.0372
    $\rho = 1.2$ 9 0.0309
    $\rho = 1.6$ 8 0.0158
     | Show Table
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    Table 3.  Algorithm (5.3) with different Cases

    No. of Iterations CPU Time
    Case Ⅰ 14 0.0045
    Case Ⅱ 14 0.0043
    Case Ⅲ 14 0.0049
     | Show Table
    DownLoad: CSV

    Table 1.  Comparison of our proposed algorithm with YNE algorithm (5.1) for different values of $N$

    $N$ 4 10 20
    Our Proposed Alg. 3.1 No. of Iter. 2 2 2
    cpu (Time) $1.0652\times 10^{-3}$ $9.0633\times 10^{-4}$ $1.2178\times 10^{-3}$
    YNE Alg. No. of Iter. 150 138 133
    cpu (Time) $8.3807\times 10^{-2}$ $0.1546$ $0.20739$
     | Show Table
    DownLoad: CSV
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