A New Accelerated Fixed-Point Algorithm for Classification and Convex Minimization Problems in Hilbert Spaces with Directed Graphs

A new accelerated algorithm for approximating the common fixed points of a countable family G-nonexpansive mappings is proposed, and weak convergence theorem based on our main results established in setting Hilbert spaces with symmetric directed graph G. As an application, we apply solving classification convex minimization problems. We also proposed to estimate weight connecting hidden layer output regularized extreme learning machine. For numerical experiments, gives higher performance accuracy testing set than that FISTA-S, FISTA, nAGA.