DOI: 10.24193/fpt-ro.2025.1.04

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

Abstract: This paper introduces and analyzes a self-adaptive inertial subgradient-like extragradient method designed to solve the bilevel split pseudomonotone variational inequality problem within the context of a common fixed-point problem, constrained by finite Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. The method incorporates a strongly monotone mapping for the upper-level problem and a pseudomonotone operator for the lower-level. We establish the strong convergence of the proposed method under mild conditions on the algorithm parameters without requiring prior knowledge of the operator norm or the coefficient of the underlying operator. Finally, we present numerical experiments to demonstrate the practicality and applicability of the proposed method. Our findings extend and improve existing results in the literature.

Key Words and Phrases: Subgradient-like extragradient method, finite Bregman relatively nonexpansive mappings, bilevel split pseudomonotone variational inequality problem, common fixed point, Bregman projection.

2010 Mathematics Subject Classification: 65Y05, 65K15, 68W10, 47H05, 47J25.

Published on-line: February 1st, 2025.

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