A General proof of the good definition of the Augmented Lagrangian method - Rezza Espinoza, Yna Consuelo (2003)
This paper presents a proof of the unicity of the sequence of multipliers generated by the Aumented Lagrangean Method with Penalties P, e P. This unicity has been tested along the last 25 years by the use of the equivalence relationship existing between the Aunented Lagrangean and Proximal Point Methods Various researchers such asRockafellar [10], Iusem 6l and Gonzaga & Castillo [2] tested this equivalence and the consequent unicity of the multipliers sequence generated by the Aumented Lagrangean Method in particular cases. The proof we are presenting includes all these cases; it is outstanding for being direct and not to use the above equivalence relation.