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In this paper, we suggest and analyze a new logarithmic–quadratic proximal alternating direction scheme for the separable constrained convex programming problem. The main contribution of this paper, the predictor is obtained via solving LQP system approximately under significantly relaxed accuracy criterion and the new iterate is obtained by using a new direction with a new step size
α
k
. Global convergence of the proposed method is proved under certain assumptions. We also reported some numerical results to illustrate the efficiency of the proposed method.