Projection-type method with line-search process for solving variational inequalities

Abstract

We propose an accelerated projection-type method for solving variational inequalities in Hilbert spaces. The method is suitable for pseudomonotone non-Lipschitz continuous operators and obtains strong convergence for iterative sequences under appropriate conditions. Based on the classical double-projection gradient method, we establish a new line-search rule and add an inertia term to improve the convergence speed of the proposed algorithm. Finally, some numerical examples are implemented to compare the proposed algorithm with the existing results, thereby verifying that our method has better performance.

Keywords:

• Hilbert space
• projection-type method
• pseudomonotone operator
• strong convergence
• variational inequality

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 47H05
• 47H07
• 47J25
• 65K15

Disclosure statement

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

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

Funding

M. Li was supported by 2023 School-level Scientific Research Project of Chongqing Industry&Trade Polytechnic (Grant No. ZR202302). P. Cholamjiak was supported by the National Research Council of Thailand under grant no. N41A640094, the Thailand Science Research and Innovation Fund and the University of Phayao (FF67).