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

Yekini Shehu; Olaniyi Iyiola

doi:10.3934/jimo.2018045

Article Contents

2019, Volume 15, Issue 1: 319-342. Doi: 10.3934/jimo.2018045

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

Yekini Shehu^1,2, , and
Olaniyi Iyiola^3,

1.
University of Nigeria, Department of Mathematics, Nsukka, Nigeria
2.
Institute of Mathematics, University of Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
3.
Department of Mathematics, Minnesota State University, Moorhead, Minnesota, USA

* Corresponding author: Yekini Shehu
* Corresponding author: Yekini Shehu

Received: June 2017

Revised: October 2017

Early access: April 2018

Published: January 2019

Abstract / Introduction Full Text(HTML) Figure(7) / Table(3) Related Papers Cited by

Abstract

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.

Keywords:

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

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

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

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

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

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Figure 13. Algorithm (5.3) Case Ⅰ

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Figure 14. Algorithm (5.3) Case Ⅱ

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Figure 15. Algorithm (5.3) Case Ⅲ

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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

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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

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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
Our Proposed Alg. 3.1	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
YNE Alg.	cpu (Time)	$8.3807\times 10^{-2}$	$0.1546$	$0.20739$

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