Convergence Analysis of Cq Methods Forsolving Split Feasibility Problems Involvinggan Operators

Optimization algorithms are fundamental to modern machine learning, data analysis, and inverse problems.Among them, CQ-type methods rely on the convergence properties of the Landweber transform.Motivated by recent generalizations of this transform, we study its behavior when applied to Generalized Averaged Nonexpansive (GAN) operators: a class extending averaged nonexpansive mappings with improved local convergence.We show that the Landweber transform preserves both the GAN structure and its regularity properties, allowing us to establish weak and strong convergence of CQ-type algorithms in this broader setting.To demonstrate the applicability of our results, we examine the matrix completion problem: a key task in recommender systems.Numerical experiments support our theory, showing global linear convergence and a local rate of order p ´1{2 q, confirming the effectiveness of the CQ algorithm for large-scale matrix completion.