Further study on a class of augmented Lagrangians of di Pillo and Grippo in nonlinear programming

In this paper, a class of augmented Lagrangians of Di Pillo and Grippo (DGALs) was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discussed between the unconstrained minimizers of DGALs on the product space of problem variables and multipliers, and the solutions of the constrained problem and the corresponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equality-constrained problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers.