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Modified inertial-type subgradient extragradient methods for variational inequalities and fixed points of finite Bregman relatively nonexpansive and demicontractive mappings
Wang, C.-S.; Ceng, L.-C.; Li, B.; Cao, S.-L.; Hu, H.-Y.; Liang, Y.-S. Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings. Axioms2023, 12, 832.
Wang, C.-S.; Ceng, L.-C.; Li, B.; Cao, S.-L.; Hu, H.-Y.; Liang, Y.-S. Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings. Axioms 2023, 12, 832.
Wang, C.-S.; Ceng, L.-C.; Li, B.; Cao, S.-L.; Hu, H.-Y.; Liang, Y.-S. Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings. Axioms2023, 12, 832.
Wang, C.-S.; Ceng, L.-C.; Li, B.; Cao, S.-L.; Hu, H.-Y.; Liang, Y.-S. Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings. Axioms 2023, 12, 832.
Abstract
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.
Copyright:
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