| Title: |
The TAO Linearly Constrained Augmented Lagrangian Method for
PDE-Constrained Optimization |
| Authors: |
Evan Gawlik,
Todd Munson,
Jason Sarich,
Stefan Wild
|
| Abstract: |
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.
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| Keywords: |
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| Thanks: |
This work was supported by the Office of Advanced Scientific Computing Research, Office of Science,
U.S. Department of Energy, under Contract DE-AC02-06CH11357, and by a DOE Computational Science
Graduate Fellowship to the lead author under grant number DE-FG02-97ER25308.
|
| Status: |
Available as Mathematics and Computer Science Division Preprint ANL/MCS-P2003-0112, January 2012. |
| Link: [PDF] |
| BibTeX: |
@techreport{Gawlik12,
title = "The {TAO} Linearly Constrained Augmented {Lagrangian} Method for
{PDE}-Constrained Optimization",
author = "Evan Gawlik and Todd Munson and Jason Sarich and Stefan M.
Wild",
institution = "Mathematics and Computer Science Division",
month = "January",
year = "2012",
type = "Preprint",
number = "ANL/MCS-P2003-0112",
url = "http://www.mcs.anl.gov/uploads/cels/papers/P2003-0112.pdf"
}
|
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