Strong convergence theorems for solving pseudo-monotone variational inequality problems and applications

Abstract

In this paper, we introduce two different kinds of iterative algorithms, which are based on the inertial Tseng's method and the viscosity method. They are intended to solve the variational inequality problems governed by the mappings of pseudo-monotone type. Strong convergence theorems are established in Hilbert spaces. Practical examples in fuzzy environment are given to show the applicability and effectiveness of the proposed algorithms.

Keywords:

• Variational inequality
• inertial extrapolation
• pseudomonotonicity
• fuzzy programming model
• Tseng's method

Acknowledgements

This paper was supported by the National Natural Science Foundation of China under Grant No.11401152.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11401152].