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.
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]
  title = "The {TAO} Linearly Constrained Augmented {Lagrangian} Method for
{PDE}-Constrained Optimization",
  author = "Evan Gawlik and Todd Munson and Jason Sarich and Stefan M.
  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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