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A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

  • * Corresponding author: Oluwatosin Temitope Mewomo

    * Corresponding author: Oluwatosin Temitope Mewomo
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  • We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.

    Mathematics Subject Classification: Primary: 47H10, 47J25; Secondary: 65J15.


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  • Figure 1.  Example 5.1, Top Left: $ N = 50 $; Top Left: $ N = 100 $; Bottom Left: $ N = 500 $; Bottom Right: $ N = 1000 $

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

    Figure 3.  Example 5.3, Top Left: Choice (i); Top Left: Choice (ii); Bottom Left: Choice (iii); Bottom Right: Choice (iv)

    Table 1.  Numerical results for Example 5.1

    No of Iteration CPU time (sec)
    $ N= 50 $ 19 0.0289
    $ N=100 $ 19 0.0386
    $ N=500 $ 41 0.1386
    $ N=1000 $ 138 0.3523
     | Show Table
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    Table 2.  Numerical results for Example 5.2

    Algorithm 3.1 Algorithm 1.1 Algorithm 1.2
    Case I CPU time (sec) 0.0021 0.0071 0.0036
    $ x_0 = 1, x_1 = 0.5 $ No of Iter. 8 22 16
    Case II CPU time (sec) 0.0021 0.0041 0.0047
    $ x_0 = -0.5, x_1 = 2 $ No. of Iter. 9 25 17
    Case III CPU time (sec) 0.0044 0.0532 0.0095
    $ x_0 = 5, x_1 = 10 $ No of Iter. 10 28 19
    Case IV CPU time (sec) 0.0062 0.0589 0.0071
    $ x_0 = -5, x_1 = 2 $ No of Iter. 10 27 19
     | Show Table
    DownLoad: CSV

    Table 3.  Numerical results for Example 5.3

    Algorithm 3.1 Algorithm 1.1
    Choice (i) CPU time (sec) 1.7859 5.1231
    No of Iter. 11 23
    Choice (ii) CPU time (sec) 1.4997 13.3981
    No. of Iter. 13 27
    Choice (iii) CPU time (sec) 2.6789 9.1093
    No of Iter. 7 12
    Choice (iv) CPU time (sec) 6.3222 24.5622
    No of Iter. 11 24
     | Show Table
    DownLoad: CSV
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