Structural optimization using augmented Lagrangian methods with secant Hessian updating

Abstract

The performance of a new implementation of the augmented Lagrangian method is evaluated on a range of explicit and structural sizing optimization problems. The results are compared with those obtained using other mathematical programming methods. The implementation uses a first-order Lagrange multiplier update and the Hessian of the augmented Lagrangian function is approximated using partitioned secant updating. A number of different secant updates are evaluated. The results show the formulation to be superior to other implementations of augmented Lagrangian methods reported in the literature and that, under certain conditions, the method approaches the performance of the state-of-the-art SQP and SAM methods. Of the secant updates, the symmetric-rank-one update, is superior to the other updates including the BFGS scheme. It is suggested that the individual function, secant updating employed may be usefully applied in contexts where structural analysis and optimization are performed simultaneously, as in the simultaneous analysis and design method. In such cases the functions are partially separable and the associated Hessians are of low rank.