DOI: 10.24193/fpt-ro.2025.2.06

Authors: L.-C. Ceng, D. Ghosh, H. ur Rehman and X. Zhao

Abstract: This research presents a novel algorithm for addressing a bilevel pseudomonotone variational inequality problem (BPVIP) constrained by a split common fixed point problem (SCFPP), employing demimetric mappings within real Hilbert spaces. The BPVIP is characterized by a strongly monotone operator at the upper-level variational inequality problem (VIP) and a pseudomonotone operator at the lower-level VIP. To address this issue, we propose a modified subgradient extragradient method that integrates an inertial term, a correction term, and a self-adaptive step size strategy. Under mild conditions, we establish the strong convergence of the proposed algorithm. Subsequently, we apply the primary result to resolve a bilevel split pseudomonotone variational inequality problem (BSPVIP). The efficacy and performance of the algorithm are demonstrated through a numerical example.

Key Words and Phrases: Modified subgradient extragradient rule, bilevel pseudomonotone variational inequality problem, pseudomonotone operator, demimetric mapping, split common fixed point problem.

2010 Mathematics Subject Classification: 65Y05, 65K15, 68W10, 47H05, 47H10.

Published on-line: May 1st, 2025.

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