On triple-adaptive projection method for bilevel split variational inequalities with CFPP constraint of finite Bregman relatively demicontractions in Banach spaces
Lu-Chuan Ceng, Cong-Shan Wang, Wang Xie, Liu-Fang Zheng, Huiying Hu, Yunshui Liang · Communications in Nonlinear Science and Numerical Simulation · 2024
In a p -uniformly convex and uniformly smooth Banach space E , the CFPP and VIP are utilized to indicate a common fixed-point problem and a variational inequality problem, respectively. We devise and discuss triple-adaptive projection method with inertial effect for resolving bilevel split VIP (BSVIP) with CFPP constraint of finite Bregman relatively demicontractive mappings in E . The method exploits the strong pseudocontractivity of one mapping at the upper-level VIP and the pseudomonotonicity of another mapping at the lower-level SVIP. We establish the strong convergence outcome for the proposed method under certain suitable restrictions on the algorithm parameters without the prior knowledge of the operator norm or the coefficient of the underlying operator. In the end, an illustrated instance is invoked to bear up the practicability and performability of the proposed method.