Augmented penalty algorithms based on BFGS secant approximations and trust regions (Q870306)

The authors study an iterative method for solving general nonlinear, equality-constrained optimization problem, based on a series of consecutive optimizations of the augmented Lagrangian function. They begin by a section where the basic definitions and introductory theorems are outlined. This is followed by section~2 which contains a description of the main algorithm which consists of an augmented Lagrangian scheme. Several elements of the proposed algorithm are presented and described in a lot of details, including the updating of the penalty function and the Hessian, the inner and outer iteration algorithms and the termination criteria. The article concludes with an indicative example, a section containing the results of numerical experimentation and a list of relevant references.