A new embedding for the augmented Lagrange method

Several algorithms such as penalty, barrier, Augmented Lagrangean and parametrical embedding approaches are used in the solution of non-linear optimization problems (P). One of these approach constructs, for each optimization problem (P), a solution including the solutions of (P) or the results of some iterative algorithms. For this parametrical problem a necessary condition for a good behavior of the continuation or to define jumps is that the parametrical problem is JJT-regular. In this work we propose an embedding for the Augmented Lagrangean Method, using the ideas of Bertsekas for this kind of algorithm and we prove that for almost every parameter, fixed the original optimization problem, the constructed parametric problem is JJT-regular. Some numerical examples to illustrate the solution are presented.