Consider two variations of the method of multipliers, or classical augmented Lagrangian method for convex programming.The proximalmethod of multipliers adjoins quadratic primal proximal terms to the augmented Lagrangian, and has a stronger primal convergence theory than the standard method. On the other hand, thealternating directionmethod of multipliers, which uses a special kind of partial minimization of the augmented Lagrangian, is conducive to the derivation of decomposition methods finding application in parallel computing. This note shows convergence a method combining the features of these two variations. The method is closely related to some algorithms of Gols'shtein. A comparison of the methods helps illustrate the close relationship between previously separate bodies of Western and Soviet literature.