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Inexact Trust-Region Methods for PDE-Constrained Optimization

  • Drew P. Kouri
  • Denis Ridzal
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 163)

Abstract

Numerical solution of optimization problems with partial differential equation (PDE) constraints typically requires inexact objective function and constraint evaluations, derivative approximations, and the use of iterative linear system solvers. Over the last 30 years, trust-region methods have been extended to rigorously, robustly, and efficiently handle various sources of inexactness in the optimization process. In this chapter, we review some of the recent advances, discuss their key algorithmic contributions, and present numerical examples that demonstrate how inexact computations can be exploited to enable the solution of large-scale PDE-constrained optimization problems.

Notes

Acknowledgements

This work was supported by DARPA EQUiPS grant SNL 014150709 and the DOE NNSA ASC ATDM program.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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Copyright information

© National Technology & Engineering Solutions of Sandia, LLC. Under the terms of Contract DE-NA0003525, there is a non-exclusive license for use of this work by or on behalf of the U.S. Government 2018

Authors and Affiliations

  1. 1.Center for Computing ResearchSandia National LaboratoriesAlbuquerqueUSA

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