Weak convergence for variational inequalities with inertial-type method

Abstract

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.

COMMUNICATED BY:

• Boris Mordukhovich

Keywords:

• Weak convergence
• inertial projection method
• variational inequality
• Hilbert spaces

2010 Mathematics Subject Classifications:

• 47H05
• 47J20
• 47J25
• 65K15
• 90C25

Acknowledgments

The authors are grateful to the anonymous referee and editor whose insightful comments and suggestions improve the earlier version of this paper.

Disclosure statement

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

Additional information

Funding

The project of the first author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160).