Two-step inertial Tseng’s extragradient methods for a class of bilevel split variational inequalities

Document Type : Research Article

Authors

• L.H.M Van ^{1, 2, 3}
• T.V. Anh ⁴

¹ Department of Mathematics and Physics, University of Information Technology, Ho Chi Minh City, Vietnam;

² Department 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;

³ Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam.

⁴ Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.

10.22067/ijnao.2025.90001.1528

Abstract

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.

Keywords

• Bilevel split variational inequality problem
• Bilevel variational inequality problem
• Split feasibility problem
• Tseng’s extragradient method

Main Subjects

• Optimization

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