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Article Contents

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

• *Corresponding author: Christian Chibueze Okeke
• 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.

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

 Citation:

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

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

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

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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