E. Gawlik, T. Munson, J. Sarich, S. M. Wild, "The TAO Linearly-Constrained Augmented Lagrangian Method for PDE-Constrained Optimization," Preprint ANL/MCS-P2003-0112, January 2012. [pdf]
This report describes a linearly-constrained augmented Lagrangian method for solving optimization problems with partial differential equation constraints. This method computes two types of directions: a Newton direction to reduce the constraint violation and reduced-space directions to improve the augmented Lagrangian merit function. The reduced-space directions are computed from limited-memory quasi Newton approximations to the reduced Hessian matrix. This method requires a minimal amount of information from the user only function, gradient, and Jacobian evaluations yet can obtain good performance. Strong scaling results are presented for some model test problems on high-performance architectures, indicating that the code scales well provided the code for the PDE constraints scales well.