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A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem

  • * Corresponding author: Oluwatosin Temitope Mewomo

    * Corresponding author: Oluwatosin Temitope Mewomo

The first author acknowledge with thanks the bursary and financial support from African Institute for Mathematical Sciences (AIMS), South Africa. The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF CoE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903)

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  • In this paper, we introduce and study a modified extragradient algorithm for approximating solutions of a certain class of split pseudo-monotone variational inequality problem in real Hilbert spaces. Using our proposed algorithm, we established a strong convergent result for approximating solutions of the aforementioned problem. Our strong convergent result is obtained without prior knowledge of the Lipschitz constant of the pseudo-monotone operator used in this paper, and with minimized number of projections per iteration compared to other results on split variational inequality problem in the literature. Furthermore, numerical examples are given to show the performance and advantage of our method as well as comparing it with related methods in the literature.

    Mathematics Subject Classification: 47H09; 47H10; 49J20; 49J40.


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  • Figure 1.  The behavior of $ \mbox{TOL}_n $ with $ \varepsilon = 10^{-3} $ for Example 4.1: Top Left: Case 1; Top Right: Case 2; Bottom Left: Case 3; Bottom Right: Case 4

    Figure 2.  The behavior of $ \mbox{TOL}_n $ with $ \varepsilon = 10^{-5} $ for Example 4.2: Top Left: Case Ⅰ; Top Right: Case Ⅱ; Bottom Left: Case Ⅲ; Bottom Right: Case Ⅳ

    Table 1.  Numerical results for Example 4.1 with $ \varepsilon = 10^{-3} $

    Cases Algorithm 3.1 Algorithm (41) Algorithm (11) Algorithm (42)
    1 CPU
    2 CPU
    3 CPU
    4 CPU
     | Show Table
    DownLoad: CSV

    Table 2.  Numerical results for Example 4.2 with $\varepsilon = 10^{-5}$

    Cases Algorithm 3.1 Algorithm (41) Algorithm (11) Algorithm (42)
    1 CPU
    2 CPU
    3 CPU
    4 CPU
     | Show Table
    DownLoad: CSV
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