Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems

New inertial algorithm for solving split common null point problem in Banach spaces

“…The main result of this paper is a new inertial algorithm which incorporates the self-adaptive step size rule to solve the split null point problems for multi-valued maximal monotone operators in Banach spaces. To some extent, the weak and strong convergence theorems of the new inertial algorithm in this paper complement the approximating methods for the solution of split common null point problem and extend and unify some results (see, e.g., Byrne et al [6], Takahashi [23], Alofi [25], Suantai et al [4] and Promluang and Kuman [5]). In addition, the numerical examples and comparisons are presented to illustrate the efficiency and reliability of our algorithms.…”

“…Step size Iter (n) K = 50, m = 2 10 , n = 2 12 10 -6 Algorithm 3.2 λ n 1881 Sitthithakerngkiet et al [23] 0.05 3262 Kazmi et al [29] 0.05 28,674 K = 40, m = 2 10 , n = 2 12 10 -6 Algorithm 3.2 λ n 1779 Sitthithakerngkiet et al [23] 0.05 2942 Kazmi et al [29] 0.05 26,488 K = 20, m = 2 10 , n = 2 12 10 -6 Algorithm 3.2 λ n 1496 Sitthithakerngkiet et al [23] 0.05 2094 Kazmi et al [29] 0.05 19,488 standard Gaussian distribution and vector b = Ax + , where is additive noise. When = 0, there is no noise in the observed data.…”

“…where t > 0 is a given constant. So, in relation with the SVIP (1.1)-(1.2), we consider B We set the parameters β n = 2n-1 2n+1 , ρ n = 3 -1 n+1 and γ n = 1 2n+1 in our Algorithm 3.2 and compare with the results of Sitthithakerngkiet et al [23] and Kazmi et al [29]. For the experiment setting we choose the following parameters: A ∈ R m×n is generated randomly with m = 2 10 , n = 2 12 , x 0 ∈ R n contains K -spikes with amplitude ±1 distributed in the whole domain randomly.…”

“…For the experiment setting we choose the following parameters: A ∈ R m×n is generated randomly with m = 2 10 , n = 2 12 , x 0 ∈ R n contains K -spikes with amplitude ±1 distributed in the whole domain randomly. In addition, for simplicity, we take f (x) = x 2 , S = I, α i = 1 i+1 in [29] and S i = I, α i = 10 -3 /(i + 1), β i = 0.5 -1/(10i + 2) in [23] and α i = i-1 i+1 , γ i = 1 i+1 in our algorithms. In addition, we take t = K in all the algorithms and the stopping criterion x n+1x n ≤ DOL with DOL = 10 -6 .…”

“…and obtained weak convergence of the sequence under suitable conditions. For more details on the methods of solving the SCNPP and the related issues in Hilbert spaces, the reader might refer to Moudafi and Thakur [19], Gibali et al [20], Censor et al [7], Shehu and Iyiola [21], Ceng et al [22], Sitthithakerngkiet et al [23]. Based on the above works, Takahashi [3,24] extended such a problem in Hilbert spaces to Banach spaces and then obtained strong convergence theorems.…”