Inertial method for split null point problems with pseudomonotone variational inequality problems

Chibueze Christian Okeke; Abdulmalik Usman Bello; Lateef Olakunle Jolaoso; Kingsley Chimuanya Ukandu

doi:10.3934/naco.2021037

Article Contents

2022, Volume 12, Issue 4: 815-836. Doi: 10.3934/naco.2021037

This issue Previous Article Dynamical complexity in a delayed Plankton-Fish model with alternative food for predators Next Article Triple-hierarchical problems with variational inequality

Inertial method for split null point problems with pseudomonotone variational inequality problems

1.
School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
2.
Mathematics Institute African University of Science and Technology, Abuja Nigeria
3.
Department of Mathematics, Federal University Dutsinma, Kastina State Nigeria
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa

^*Corresponding author: Christian Chibueze Okeke
^*Corresponding author: Christian Chibueze Okeke

Received: March 31, 2021

Revised: August 31, 2021

Early access: September 2021

Published: December 2022

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Abstract

This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.

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Mathematics Subject Classification: Primary: 47H10; 49J20; Secondary: 49J40.

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Figure 1. Example 5.1, Top Left: Case I; Top Right: Case II; Bottom: Case III

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

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Table 1. Computational result for Example 5.1

		Case I	Case II	Case III
Algo. 3.3 ($ \alpha =5 $)	No of Iter.	7	8	8
	CPU time (sec)	0.034	0.0050	0.0034
Algo. 3.3 ($ \alpha =3 $)	No of Iter.	13	14	14
	CPU time (sec)	0.0109	0.0160	0.0076
NUMA	No of Iter.	51	54	58
	CPU time (sec)	0.0249	0.0296	0.0288

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Table 2. Computational result for Example 5.2

		Case I	Case II	Case III
Algo. 3.3 ($ \alpha =5 $)	No of Iter.	8	16	90
	CPU time (sec)	0.0096	0.0223	0.0425
Algo. 3.3 ($ \alpha =3 $)	No of Iter.	8	19	323
	CPU time (sec)	0.0035	0.00089	0.4394
NUMA	No of Iter.	8	17	69
	CPU time (sec)	0.0051	0.0084	0.0257

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