Second order correction for augmented Lagrangian subproblems

DAMIÁN FERNÁNDEZ

Luis Correia-PI

Workshop; IX Brazilian Workshop on Continuous Optimization; 2012

Universidade Federal de Piauí

An augmented Lagrangian method is based on a sequential (inexact) minimization of the augmented Lagrangian function. Computationally, the minimization is performed by an outer solver that performs an undetermined number of iterations in order to satisfy a prescribed tolerance. In this work we show that a suitable tolerance can be reached by solving only two constrained quadratic problems. The fist one is a Newtonian iteration for the problem of minimize the augmented Lagrangian function. The second one is the well-known second order correction for the sequential quadratic programming method. While the first problem improves optimality, the second decrease the distance to stationary points. We show that the proposed method is well-defined and locally convergent.