An augmented Lagrangian trust region method for equality constrained optimization

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate model of the augmented Lagrangian function to generate the next iterate. A condition is introduced to decide whether the Lagrange multiplier should be updated. We also suggest a new strategy for adjusting the penalty parameters. Global convergence of this method is established under mild conditions. Furthermore, we analyze the behavior of penalty parameters and figure out in which case they will be bounded from above. Numerical experiments on problems from the CUTEr set collection reveal that our method is very promising.