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We analyze the rate of convergence of the proximal method of multipliers for non-convex nonlinear programming problems. First, we prove, under the strict complementarity condition, that the rate of convergence of the proximal method of multipliers is linear and the ratio constant is proportional to 1/c when the ratio ‖ (μ 0 , λ 0) − (μ ¯ , λ ¯) ‖ / c is small enough, which implies that the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to + ∞. Second, we prove that, without strict complementarity condition, the rate of convergence of the proximal method of multipliers is proportional to 1/c when c exceeds a threshold. [ABSTRACT FROM AUTHOR]