A BREGMAN PROJECTION ALGORITHM WITH SELF ADAPTIVE STEP SIZES FOR SPLIT VARIATIONAL INEQUALITY PROBLEMS INVOLVING NON-LIPSCHITZ OPERATORS

Abstract

The purpose of this paper is to investigate a Bregman projection algorithm for solving the split variational inequality problem governed by pseudomonotone and not necessarily Lipschitz continuous operators in real Hilbert spaces. The proposed algorithm is motivated by the ideas of the Halpern method, the CQ method, and Tseng's extragradient method. The step size sequences are determined by employing Armijo line search techniques. The strong convergence theorem is established without the prior knowledge of the operator norm and the Lipschitz continuous assumption on the operators involved. Some numerical experiments with graphical illustrations are presented to demonstrate the effectiveness and the performance of our proposed algorithm in comparison with some existing ones. © 2024 Journal of Nonlinear and Variational Analysis.