Modified inertial-type subgradient extragradient methods for variational inequalities and fixed points of finite Bregman relatively nonexpansive and demicontractive mappings
Cong-Shan Wang, Lu-Chuan Ceng, Bing Li, Sheng-Long Cao, Huiying Hu, Yunshui Liang · Preprints.org · 2023
In this paper, we design two inertial-type subgradient extragradient algorithms with line-search process for solving the pseudomonotone variational inequality problems (VIPs) and common fixed-point problem (CFPP) of finite Bregman relatively nonexpansive mapping and a Bregman relatively demicontractive mapping in p-uniformly convex and uniformly smooth Banach spaces, which are more general than Hilbert spaces. Under mild conditions, we derive weak and strong convergence of the suggested algorithms to a common solution of the VIPs and CFPP, respectively. Additionally, an illustrated example is furnished to back up the feasibility and implementability of our proposed methods.