The TAO Linearly-Constrained Augmented Lagrangian Method for PDE-Constrained Optimization
|Title||The TAO Linearly-Constrained Augmented Lagrangian Method for PDE-Constrained Optimization|
|Publication Type||Journal Article|
|Year of Publication||2012|
|Authors||Gawlik, E, Munson, TS, Sarich, J, Wild, SM|
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.