# American Institute of Mathematical Sciences

• Previous Article
A novel methodology for portfolio selection in fuzzy multi criteria environment using risk-benefit analysis and fractional stochastic
• NACO Home
• This Issue
• Next Article
Convergence of interval AOR method for linear interval equations
doi: 10.3934/naco.2021037
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## 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

Received  April 2021 Revised  September 2021 Early access September 2021

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.

Citation: Chibueze Christian Okeke, Abdulmalik Usman Bello, Lateef Olakunle Jolaoso, Kingsley Chimuanya Ukandu. Inertial method for split null point problems with pseudomonotone variational inequality problems. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2021037
##### References:

show all references

##### References:
Example 5.1, Top Left: Case I; Top Right: Case II; Bottom: Case III
Example 5.2, Top Left: Case I; Top Right: Case II; Bottom: Case III
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
 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
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
 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
 [1] Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021046 [2] Grace Nnennaya Ogwo, Chinedu Izuchukwu, Oluwatosin Temitope Mewomo. A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021011 [3] Augusto VisintiN. On the variational representation of monotone operators. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 909-918. doi: 10.3934/dcdss.2017046 [4] Ai-Ling Yan, Gao-Yang Wang, Naihua Xiu. Robust solutions of split feasibility problem with uncertain linear operator. Journal of Industrial & Management Optimization, 2007, 3 (4) : 749-761. doi: 10.3934/jimo.2007.3.749 [5] S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155 [6] Jamilu Abubakar, Poom Kumam, Abor Isa Garba, Muhammad Sirajo Abdullahi, Abdulkarim Hassan Ibrahim, Wachirapong Jirakitpuwapat. An efficient iterative method for solving split variational inclusion problem with applications. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021160 [7] Marta García-Huidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313-319. doi: 10.3934/proc.2003.2003.313 [8] Gang Cai, Yekini Shehu, Olaniyi S. Iyiola. Inertial Tseng's extragradient method for solving variational inequality problems of pseudo-monotone and non-Lipschitz operators. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021095 [9] Abbas Ja'afaru Badakaya, Aminu Sulaiman Halliru, Jamilu Adamu. Game value for a pursuit-evasion differential game problem in a Hilbert space. Journal of Dynamics & Games, 2022, 9 (1) : 1-12. doi: 10.3934/jdg.2021019 [10] T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks & Heterogeneous Media, 2008, 3 (3) : 675-689. doi: 10.3934/nhm.2008.3.675 [11] Junfeng Yang. Dynamic power price problem: An inverse variational inequality approach. Journal of Industrial & Management Optimization, 2008, 4 (4) : 673-684. doi: 10.3934/jimo.2008.4.673 [12] Jianlin Jiang, Shun Zhang, Su Zhang, Jie Wen. A variational inequality approach for constrained multifacility Weber problem under gauge. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1085-1104. doi: 10.3934/jimo.2017091 [13] Yekini Shehu, Olaniyi Iyiola. On a modified extragradient method for variational inequality problem with application to industrial electricity production. Journal of Industrial & Management Optimization, 2019, 15 (1) : 319-342. doi: 10.3934/jimo.2018045 [14] Mostafa Mbekhta. Representation and approximation of the polar factor of an operator on a Hilbert space. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 3043-3054. doi: 10.3934/dcdss.2020463 [15] P. Chiranjeevi, V. Kannan, Sharan Gopal. Periodic points and periods for operators on hilbert space. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 4233-4237. doi: 10.3934/dcds.2013.33.4233 [16] Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems & Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169 [17] Mohammad Eslamian, Ahmad Kamandi. A novel algorithm for approximating common solution of a system of monotone inclusion problems and common fixed point problem. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021210 [18] Soumia Saïdi. On a second-order functional evolution problem with time and state dependent maximal monotone operators. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021034 [19] Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013 [20] Yazheng Dang, Jie Sun, Honglei Xu. Inertial accelerated algorithms for solving a split feasibility problem. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1383-1394. doi: 10.3934/jimo.2016078

Impact Factor:

## Tools

Article outline

Figures and Tables