On problems of augmentation of Lagrangians in penalty functions of nonlinear programming

Abstract

We modify Pillow and Grippo's work in which a minimization problem with equality constraints is treated via an unconstrained minimization technique in which a new class of augmented Lagrangians is introduced and make a suitable use of a method analogous to the penalty function used by Mangasarian "ia the Wolfe dual of the original minimization problem. For simplicity we treat the case with equality constraints. We believe that this method can be generalized for inequality constrained problems as well. The advantage of the new method is that the penalty parameter remains finite as observed by Mangasarian.