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.
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).