Generalized Bregman Projection Algorithms for Solving Nonlinear Split Feasibility Problems in Infinite-Dimensional Spaces

TL;DR

This paper develops generalized Bregman projection algorithms that improve solving nonlinear split feasibility problems in infinite-dimensional spaces, demonstrating better convergence and efficiency through theoretical analysis and numerical experiments.

Contribution

It introduces a novel combination of Bregman projections, proximal steps, and inertial terms for nonlinear split feasibility problems in infinite-dimensional Hilbert spaces.

Findings

Strong convergence under mild assumptions

Enhanced efficiency over classical methods

Robust performance in numerical experiments

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.