The Augmented Lagrangian Method (ALM), firstly proposed in 1969, remains a vital framework in large-scale constrained optimization. This paper addresses a linearly constrained composite convex minimization problem and presents a general proximal ALM that incorporates both Nesterov acceleration and relaxed acceleration, while enjoying a proximal-indefinite term. Under mild assumptions (potentially without requiring prior knowledge of the objective function’s strong convexity modulus), we establish global convergence and derive an O(1/k^2 ) nonergodic convergence rate for the Lagrangian residual, the objective gap, and the constraint violation, where $k$ denotes the iteration number. Numerical experiments on testing large-scale sparse signal reconstruction tasks demonstrate the method’s superior performance against several well-established baselines.