A New Extragradient Method for Strongly Pseudomonotone Variational Inequalities

ABSTRACT

This article proposes a new extragradient solution method for strongly pseudomonotone variational inequalities. A detailed analysis of the iterative sequences’ convergence and of the range of applicability of the method is provided. Moreover, an interesting class of strongly pseudomonotone infinite dimensional variational inequality problems is considered.

KEYWORDS:

• Convergence
• monotonicity
• new extragradient method
• strong pseudomonotonicity
• variational inequality

MATHEMATICS SUBJECT CLASSIFICATION:

• 47J20
• 49J40
• 49M30

Acknowledgements

The guidance of Prof. N. D. Yen and Dr. T. C. Dieu is gratefully acknowledged. The author would like to thank the anonymous referees and the Editor in Chief, Professor Zuhair Nashed, for their constructive comments which significantly improve the presentation of the article.