An Augmented Lagrangian Trust Region Method with a Bi-Object Strategy (Journal of Computational Mathematics, 2018)
An augmented Lagrangian trust region method with a bi-object strategy is proposed forsolving nonlinear equality constrained optimization, which falls in between penalty-typemethods and penalty-free ones. At each iteration, a trial step is computed by minimizinga quadratic approximation model to the augmented Lagrangian function within a trustregion. The model is a standard trust region subproblem for unconstrained optimizationand hence can efficiently be solved by many existing methods. To choose the penaltyparameter, an auxiliary trust region subproblem is introduced related to the constraintviolation. It turns out that the penalty parameter need not be monotonically increasingand will not tend to infinity. A bi-object strategy, which is related to the objective functionand the measure of constraint violation, is utilized to decide whether the trial step will beaccepted or not. Global convergence of the method is established under mild assumptions.Numerical experiments are made, which illustrate the efficiency of the algorithm on variousdifficult situations.