Generalized Bregman Projection Algorithms for Solving Nonlinear Split Feasibility Problems in Infinite-Dimensional Spaces (2505.11537v1)

Abstract: This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and adaptive inertial terms to enhance convergence. Strong convergence is established under mild assumptions, and numerical experiments demonstrate the efficiency and robustness of the proposed algorithms in comparison to classical methods. These results contribute to advancing optimization techniques for nonlinear and high-dimensional problems.