Existence of Local Saddle Points for a New Augmented Lagrangian Function

Abstract EN

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints.

The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed.

In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions.