In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed algorithm performs better than some well-established methods. INDEX TERMS Convex

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... ization, proximal point algorithm, complexity, signal processing. JIANCHAO BAI received the B.S. degree from Yan'an University, in 2012, the M.S. degree from the Guilin University of Electronic Technology, in 2015, and the Ph.D. degree from Xi'an Jiaotong University, in 2018. He is currently an Associate Professor with the Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China. His research interests include optimization theories and their applications, which aims to develop some efficient first-order algorithms for solving nonlinear convex/nonconvex programming problems in signal processing, statistical learning, and machine learning.