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Title: An introduction to partial differential equations constrained optimization

Abstract

Partial differential equation (PDE) constrained optimization is designed to solve control, design, and inverse problems with underlying physics. A distinguishing challenge of this technique is the handling of large numbers of optimization variables in combination with the complexities of discretized PDEs. Over the last several decades, advances in algorithms, numerical simulation, software design, and computer architectures have allowed for the maturation of PDE constrained optimization (PDECO) technologies with subsequent solutions to complicated control, design, and inverse problems. This special journal edition, entitled “PDE-Constrained Optimization”, features eight papers that demonstrate new formulations, solution strategies, and innovative algorithms for a range of applications. In particular, these contributions demonstrate the impactfulness on our engineering and science communities. This paper offers short remarks to provide some perspective and background for PDECO, in addition to summaries of the eight papers.

Authors:
 [1];  [2]
  1. Technische Univ. of Munich (Germany)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1478062
Report Number(s):
[SAND-2018-8151J]
[Journal ID: ISSN 1389-4420; 666187]
Grant/Contract Number:  
[AC04-94AL85000]
Resource Type:
Accepted Manuscript
Journal Name:
Optimization and Engineering
Additional Journal Information:
[ Journal Volume: 19; Journal Issue: 3]; Journal ID: ISSN 1389-4420
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Ulbrich, Michael, and Bloemen Waanders, Bart van. An introduction to partial differential equations constrained optimization. United States: N. p., 2018. Web. doi:10.1007/s11081-018-9398-1.
Ulbrich, Michael, & Bloemen Waanders, Bart van. An introduction to partial differential equations constrained optimization. United States. doi:10.1007/s11081-018-9398-1.
Ulbrich, Michael, and Bloemen Waanders, Bart van. Thu . "An introduction to partial differential equations constrained optimization". United States. doi:10.1007/s11081-018-9398-1. https://www.osti.gov/servlets/purl/1478062.
@article{osti_1478062,
title = {An introduction to partial differential equations constrained optimization},
author = {Ulbrich, Michael and Bloemen Waanders, Bart van},
abstractNote = {Partial differential equation (PDE) constrained optimization is designed to solve control, design, and inverse problems with underlying physics. A distinguishing challenge of this technique is the handling of large numbers of optimization variables in combination with the complexities of discretized PDEs. Over the last several decades, advances in algorithms, numerical simulation, software design, and computer architectures have allowed for the maturation of PDE constrained optimization (PDECO) technologies with subsequent solutions to complicated control, design, and inverse problems. This special journal edition, entitled “PDE-Constrained Optimization”, features eight papers that demonstrate new formulations, solution strategies, and innovative algorithms for a range of applications. In particular, these contributions demonstrate the impactfulness on our engineering and science communities. This paper offers short remarks to provide some perspective and background for PDECO, in addition to summaries of the eight papers.},
doi = {10.1007/s11081-018-9398-1},
journal = {Optimization and Engineering},
number = [3],
volume = [19],
place = {United States},
year = {2018},
month = {8}
}

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Works referenced in this record:

Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation
journal, June 2018

  • Kärcher, Mark; Boyaval, Sébastien; Grepl, Martin A.
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9389-2

A PDE-constrained optimization approach for topology optimization of strained photonic devices
journal, July 2018


Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting
journal, June 2018

  • Antil, Harbir; Nochetto, Ricardo H.; Venegas, Pablo
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9392-7

Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics
journal, June 2018

  • Herzog, Roland; Riedel, Ilka; Uciński, Dariusz
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9391-8

A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn–Hilliard–Navier–Stokes system
journal, June 2018

  • Hintermüller, Michael; Hinze, Michael; Kahle, Christian
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9393-6

Designing polymer spin packs by tailored shape optimization techniques
journal, June 2018

  • Leithäuser, Christian; Pinnau, René; Feßler, Robert
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9396-3

PDE-constrained optimization in medical image analysis
journal, June 2018

  • Mang, Andreas; Gholami, Amir; Davatzikos, Christos
  • Optimization and Engineering, Vol. 19, Issue 3
  • DOI: 10.1007/s11081-018-9390-9