In the paper [Torrealba, E.M.R. et al. Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem. EJOR, 299(1) 46--59, 2021] an augmented Lagrangian algorithm was proposed for resource allocation problems with the intriguing characteristic that instead of solving the box-constrained augmented Lagrangian subproblem, they propose projecting the solution of the unconstrained subproblem onto such box. The paper suggests that a global convergence theorem was proved for such a method, however, this is somewhat contrary to usual augmented Lagrangian theory, as this strategy can fail in solving the augmented Lagrangian subproblems. In this note we show that the proposed method may indeed fail and we pinpoint the inconsistency of the aforementioned paper as they use two different projections: one for obtaining their convergence results and other in their implementation. Regardless of the lack of theory, their strategy works remarkably well in some classes of problems, thus, we propose an hybrid method which uses their idea as a starting point heuristics, switching to a standard augmented Lagrangian method when the heuristics fails in improving the KKT residual of the problem. We provide numerical results showing that this strategy is successful in accelerating the standard method.

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