Using automatic differentiation for second-order matrix-free methods in PDE-constrained optimization.

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Classical methods of constrained optimization are often based on the assumptions that projection onto the constraint manifold is routine but accessing second-derivative information is not. Both assumptions need revision for the application of optimization to systems constrained by partial differential equations, in the contemporary limit of millions of state variables and in the parallel setting. Large-scale PDE solvers are complex pieces of software that exploit detailed knowledge of architecture and application and cannot easily be modified to fit the interface requirements of a blackbox optimizer. Furthermore, in view of the expense of PDE analyses, optimization methods not using second derivatives ... continued below

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Hovland, P. D.; Keyes, D. E.; McInnes, L. C. & Samyono, W. November 20, 2000.

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Classical methods of constrained optimization are often based on the assumptions that projection onto the constraint manifold is routine but accessing second-derivative information is not. Both assumptions need revision for the application of optimization to systems constrained by partial differential equations, in the contemporary limit of millions of state variables and in the parallel setting. Large-scale PDE solvers are complex pieces of software that exploit detailed knowledge of architecture and application and cannot easily be modified to fit the interface requirements of a blackbox optimizer. Furthermore, in view of the expense of PDE analyses, optimization methods not using second derivatives may require too many iterations to be practical. For general problems, automatic differentiation is likely to be the most convenient means of exploiting second derivatives. We delineate a role for automatic differentiation in matrix-free optimization formulations involving Newton's method, in which little more storage is required than that for the analysis code alone.

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  • 3rd International Conference/Workshop on Automatic Differentiation: From Simulation to Optimization, Nice (FR), 06/19/2000--06/23/2000; Other Information: PBD: 20 Nov 2000; PBD: 20 Nov 2000

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  • Report No.: ANL/MCS/CP-103457
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 768628
  • Archival Resource Key: ark:/67531/metadc724306

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  • November 20, 2000

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 29, 2016, 3:24 p.m.

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Hovland, P. D.; Keyes, D. E.; McInnes, L. C. & Samyono, W. Using automatic differentiation for second-order matrix-free methods in PDE-constrained optimization., article, November 20, 2000; Illinois. (digital.library.unt.edu/ark:/67531/metadc724306/: accessed December 15, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.