VISCOSITY-BASED GRADIENT TECHNIQUES FOR SPLITFEASIBILITY PROBLEMS

Abstract

 The Split Feasibility Problem (SFP) is a key optimization model
with diverse applications in fields such as inverse problems, signal processing, and medical imaging. This paper presents novel viscosity algorithms for solving the SFP in infinite-dimensional Hilbert spaces. Building on existing methods, we introduce new inertial techniques to improve convergence properties. The proposed algorithms feature adaptive step size strategies, which eliminate the need for prior knowledge of operator norms, ensuring greater computational efficiency. Strong convergence results are demonstrated under mild assumptions.
These results generalize many existing findings in the literature.