In a recent paper, we introduced a new algorithm of inexact-restoration type for solving minimization problems with equality constraints and bounds on the variables (see [12]). The procedure to force global convergence of this algorithm makes use of an augmented Lagrangian merit function. Here, the same ideas are applied to the problems where inequality constraints are explicitly given. We prove global convergence of the new method but, perhaps surprisingly, the merit function does not allow us to use arbitrary estimates of Lagrange multipliers.