Inertial self-adaptive parallel extragradient-type method for common solution of variational inequality problems

ABSTRACT

In this paper, we introduce a new inertial self-adaptive parallel subgradient extragradient method for finding common solution of variational inequality problems with monotone and Lipschitz continuous operators. The stepsize of the algorithm is updated self-adaptively at each iteration and does not involve a line search technique nor a prior estimate of the Lipschitz constants of the cost operators. Also, the algorithm does not required finding the farthest element of the finite sequences from the current iterate which has been used in many previous methods. We prove a strong convergence result and provide some applications of our result to other optimization problems. We also give some numerical experiments to illustrate the performance of the algorithm by comparing with some other related methods in the literature.

KEYWORDS:

• Common solution
• variational inequality
• monotone operators
• self-adaptive
• parallel extragradient method

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 49J35
• 90C47

Acknowledgments

The authors sincerely thank the editor and anonymous referees for the careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The authors acknowledge with thanks the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research.

Disclosure statement

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

Additional information

Funding

This research is supported by the postdoctoral research fund at the Sefako Makgatho Health Science University, Pretoria, South Africa.