Inertial modified projection algorithm with self-adaptive technique for solving pseudo-monotone variational inequality problems in Hilbert spaces

Abstract

For solving pseudo-monotone variational inequality problems in Hilbert spaces, we introduce a new algorithm with self-adaptive technique. The algorithm is based on the projection method and inertial method. The strong convergence theorem is established under some appropriate conditions. Finally, we provide some numerical experiments to illustrate the effectiveness and advantages of the proposed algorithm.

Keywords:

• Variational inequality problem
• projection method
• inertial method
• hybrid algorithm
• pseudo-monotone operator
• self-adaptive technique

2010 Mathematics Subject Classifications:

• 47H05
• 90C33

Acknowledgments

The authors are grateful to the referees for useful suggestions which improved the contents of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China [No. 2019ASP-TJ02].