Le, Van, Tran, Anh. (1404). Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities. سامانه مدیریت نشریات علمی, (), -. doi: 10.22067/ijnao.2025.90001.1528
Van Huynh My Le; Anh Viet Tran. "Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities". سامانه مدیریت نشریات علمی, , , 1404, -. doi: 10.22067/ijnao.2025.90001.1528
Le, Van, Tran, Anh. (1404). 'Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22067/ijnao.2025.90001.1528
Le, Van, Tran, Anh. Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities. سامانه مدیریت نشریات علمی, 1404; (): -. doi: 10.22067/ijnao.2025.90001.1528
Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities
Iranian Journal of Numerical Analysis and Optimization
1Department of Mathematics and Physics, University of Information Technology, Ho Chi Minh City, Vietnam.
2Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam.
3Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam.
4Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
چکیده
This work presents a two-step inertial Tseng’s extragradient method with a self-adaptive step size for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. This algorithm only requires two projections per iteration, enhancing its practicality. We establish a strong convergence theorem for the method, showing that it effectively tackles the BSVIP without necessitating prior knowledge of the Lipschitz or strongly monotone constants associated with the mappings. Additionally, the implementation of this method removes the need to compute or estimate the norm of the given operator, a task that can often be challenging in practical situations. We also explore specific cases to demonstrate the versatility of the method. Finally, we present an application of the split minimum norm problem in production and consumption systems and provide several numerical experiments to validate the practical implementability of the proposed algorithms.