Training of extreme learning machine network based on novel generalized inertial forward-reflected-backward splitting algorithm

In this paper, we consider the monotone inclusion problems involving three operators using a novel generalized inertial forward-reflected-backward splitting algorithm (IRFBA) in real Hilbert spaces. We propose a new double inertial extrapolation step that enhances the acceleration of the splitting algorithm and presents a trade-off between the parameters of the inertial step. In contrast to the existing literature, the proposed method does not require a prior estimate of the Lipschitz constant of the operators in the summand. Afterward, the weak and linear convergence of the method is studied under mild conditions. We validate the performance of our proposed IFRBA algorithm using a real-world machine learning dataset. To assess its effectiveness, we compared our algorithm with three other state-of-the-art training algorithms. In the comparison, we formulated regression problems based on extreme learning machine concepts and conducted multiple experiments to examine the robustness of our IFRBA algorithm thoroughly. The analysis of various metrics, including average mean square error, coefficient of determination, average mean absolute error, average root Mean square error, and convergence speed, consistently demonstrated the efficient performance of our proposed IFRBA algorithm.