A New Halpern-Type Bregman Projection Method for Solving Variational Inequality Problems in Reflexive Banach Space

This paper proposes a new Halpern-type inertial subgradient extragradient method with Bregman distance for solving variational inequality problems in a real reflexive Banach space. The proposed algorithm is determined by a self-adaptive technology, which avoids the difficulty of adequately estimating the Lipschitz constant of monotone operators in practical applications. Weak and strong convergence theorems for our algorithm are established, and several numerical experiments are discussed to verify the validity and adaptability.