Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem

Abstract

In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.

Keywords:

• Strong convergence
• variational inequality problem
• pseudomonotone mapping
• minimum-norm solution
• optimal control problem

2010 AMS Subject Classifications:

• 47H09
• 47H10
• 47J25
• 47J30

Acknowledgments

P. Sunthrayuth would like to thank Rajamangala University of Technology Thanyaburi (RMUTT). The authors are grateful to the two anonymous referees for their suggestions, which helped us to improve the quality of the initial manuscript.

Disclosure statement

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

Additional information

Funding

B. Tan thanks for the financial support from the China Scholarship Council (CSC No. 202106070094). P. Cholamjiak was supported by University of Phayao and Thailand Science Research and Innovation grant no. FF66-UoE and Y.J. Cho thank Thailand Science Research and Innovation (IRN62W0007).