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A convex minimization problem in the form of the sum of two proper lower-semicontinuous convex functions has received much attention from the community of optimization due to its broad applications to many disciplines, such as machine learning, regression and classification problems, image and signal processing, compressed sensing and optimal control. Many methods have been proposed to solve such problems but most of them take advantage of Lipschitz continuous assumption on the derivative of one function from the sum of them. In this work, we introduce a new accelerated algorithm for solving the mentioned convex minimization problem by using a linesearch technique together with a viscosity inertial forward–backward algorithm (VIFBA). A strong convergence result of the proposed method is obtained under some control conditions. As applications, we apply our proposed method to solve regression and classification problems by using an extreme learning machine model. Moreover, we show that our proposed algorithm has more efficiency and better convergence behavior than some algorithms mentioned in the literature.

A New Machine Learning Algorithm Based on Optimization Method for Regression and Classification Problems