Article Contents
Article Contents

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

• * Corresponding author: Yekini Shehu
• 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:

• 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

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

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) $8.3807\times 10^{-2}$ $0.1546$ $0.20739$

Figures(7)

Tables(3)