Results on Exactness Properties of the HP-ALF for Inequality Constraints

In this paper, the Hestenes-Powell augmented Lagrangian function (HP-ALF) is again considered, for solving inequality constrained problems via unconstrained minimization techniques. Under suitable assumptions, the relationships are established between the solution of the original constrained problem and the unconstrained minimization of the HP-ALF on the space of problem variables or on the product space of problem variables and multipliers. Especially, some new results on exactness properties of the HP-ALF are given. The properties exhibited in this paper indicate more precisely that the HP-ALF is an exact multiplier penalty function, and a solution of the original constrained problem and the corresponding values of the Lagrange multipliers can be found by the well known method of multipliers