It has been demonstrated that the alternating direction method of multipliers (ADMM) with logarithmic-quadratic proximal (LQP) regularization is efficient in solving a specific class of separable convex optimization problems. This method capitalizes on the individual separable properties and transforms the constrained subproblems into more manageable unconstrained subproblems during the iterative process. In this paper, we investigate the application of the inertial proximal point method and focus on studying the inertial ADMM and symmetric ADMM with LQP regularization for solving constrained separable convex optimization problems. These approaches employ ADMM or symmetric ADMM on extrapolated points with appropriate step sizes to accelerate the convergence rate. Under some mild conditions, we establish the global convergence of the proposed methods.