New inertial method for generalized split variational inclusion problems

Preeyanuch Chuasuk; Ferdinard Ogbuisi; Yekini Shehu; Prasit Cholamjiak

doi:10.3934/jimo.2020123

Article Contents

2021, Volume 17, Issue 6: 3357-3371. Doi: 10.3934/jimo.2020123

This issue Previous Article C-eigenvalue intervals for piezoelectric-type tensors via symmetric matrices Next Article On the

$ BMAP_1, BMAP_2/PH/g, c $

retrial queueing system

New inertial method for generalized split variational inclusion problems

1.
Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
2.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban South Africa
3.
University of Nigeria, Department of Mathematics, Nsukka, Nigeria
4.
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People's Republic of China
5.
School of Science, University of Phayao, Phayao, Thailand

^* Corresponding author: F. U. Ogbuisi
^* Corresponding author: F. U. Ogbuisi

Received: November 30, 2019

Revised: December 31, 2019

Early access: June 2020

Published: November 2021

The work of the second author is based on the research supported wholly by the National Research Foundation (NRF) of South Africa (Grant Numbers: 111992). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF. This work was supported by Thailand Science Research and Innovation grant no. IRN62W0007 and Thailand Research Fund and University of Phayao grant no. RSA6180084

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Abstract

The purpose of this paper is to introduce a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. We prove that the generated sequence converges weakly to the solution of the considered problem under some mild conditions. The major contributions of our results are: (ⅰ) to increase the rate of convergence of the method for solving split variational inclusion problem through the inertial extrapolation step, (ⅱ) to relax the choice of the inertial factor and show the inertial factor can be chosen greater than 1/3 unlike what is previously known before for inertial proximal point method in the literature (ⅲ) to show the numerical efficiency and superiority of our proposed method through some test example.

Keywords:

Mathematics Subject Classification: Primary: 49J53, 65K10; Secondary: 49M37, 90C25.

Citation:

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Table 1. The results of Algorithm 3.1 with the difference of $\gamma_{n}$

N	N.P.	$\gamma_{n}$	Average iteration	Average times
10	10	$\frac{n}{2(n+1)}$	1385	36.2813
10	10	1	734	18.9375
10	10	2	387	9.5625
10	10	3	265	6.6094
10	10	$\frac{3(n+1)}{(n+2)}$	202	5.0625

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Table 2. The results computed on Algorithm 3.1 and the method in [47]

N	N.P.	Average iteration		Average times
		Algorithm 3.1	Method in [47]	Algorithm 3.1	Method in [47]
10	10	202	921	5.0625	30.4219
20	10	114	14319	3.0781	403.1563
30	10	72	23114	2.6250	969.2813
50	10	43	26894	1.5625	1000.0190
100	10	17	45443	0.4844	3000.4453

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Table 3. The results of Algorithm 3.1 with the difference of $\theta_{n}$

$\theta_{n}$	Average iteration	Average times
0	431	4.9200
0.1	236	2.4900
0.25	223	2.300
0.5	80	0.6600
0.75	71	0.5538
0.9	54	0.4600
1	41	0.3700

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Table 4. The results computed on Algorithm 3.1 and the method in [43]

N	Average iteration		Average times
	Algorithm 3.1	Method in [43]	Algorithm 3.1	Method in [43]
10	96	206	0.7400	1.9600
20	77	150	0.6100	1.3300

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Table 5. The results computed in Algorithm 3.1 and the method in [44]

N	Average iteration		Average times
	Algorithm 3.1	Method in [44]	Algorithm 3.1	Method in [44]
10	38	150	0.7600	4.1100
20	10	129	0.2200	2.3600

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