Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications

Abstract

We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.

Keywords:

• Variational inequality problem
• projection and contraction method
• subgradient extragradient method
• optimal control problem
• signal processing problem

Mathematics Subject Classifications (2010):

• 47J20
• 47J25
• 47J30
• 68W10
• 65K15

Acknowledgments

The authors are deeply grateful to the Editor and the anonymous referee for their careful reading, excellent insights and comments, which helped us to improve the quality of the original manuscript considerably.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

Bing Tan thanks the China Scholarship Council for the financial support (CSC No. 202106070094).