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