In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further use it to solve the separable convex optimization problem with linear constraints. Which is different to the existing customized proximal point algorithms, the proposed algorithm does not involve any relaxation step but still ensure the convergence. We obtain the particular iteration schemes and the unified variational inequality where the parameter matrix is symmetric and positive semi-definite, then the global convergence and a worst-case convergence rate of the proposed method are proven under some mild assumptions. Finally some numerical experiments show that, the proposed method is valid and high efficient comparing with some existing state-of-the-art methods.
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