Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications

Abstract

In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.

Keywords:

• Variational inequality problem
• projection and contraction method
• inertial extragradient method
• pseudomonotone mapping
• uniformly continuous mapping

Mathematics Subject Classifications:

• 47H05
• 47H09
• 49J15
• 47J20
• 65K15

Acknowledgments

The authors are very grateful to the anonymous referees for their useful comments, which helped us to improve the quality of the initial manuscript.

Disclosure statement

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