Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities

ABSTRACT

We propose two modified Tseng's extragradient methods (also known as Forward–Backward–Forward methods) for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under mild and standard conditions, we obtain the weak and strong convergence of the proposed methods. Numerical examples for illustrating the behaviour of the proposed methods are also presented

KEYWORDS:

• Forward–Backward–Forward method
• extragradient method
• Mann-type method
• variational inequality
• pseudo-monotone operator

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47J20
• 47J05
• 47J25

Acknowledgments

We thank the anonymous reviewers for their constructive comments which help us improve the presentation of this paper. We would also like to thank the Associate Editor for the efficient handling of the review process.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2017.315] and the Austrian Science Fund (FWF) [grant number M2499-N32].