An introduction to partial differential equations constrained optimization

Ulbrich, Michael; Bloemen Waanders, Bart van

doi:10.1007/s11081-018-9398-1

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:

Ulbrich, Michael ^[1]; Bloemen Waanders, Bart van ^[2]

Technische Univ. of Munich (Germany)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Thu Aug 09 00:00:00 EDT 2018

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.

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                    Ulbrich, Michael, & Bloemen Waanders, Bart van. An introduction to partial differential equations constrained optimization.  United States.  https://doi.org/10.1007/s11081-018-9398-1

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                    Ulbrich, Michael, and Bloemen Waanders, Bart van. Thu .  
"An introduction to partial differential equations constrained optimization".  United States.  https://doi.org/10.1007/s11081-018-9398-1.  https://www.osti.gov/servlets/purl/1478062.

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@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         = {Thu Aug 09 00:00:00 EDT 2018},

  month        = {Thu Aug 09 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

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https://doi.org/10.1007/s11081-018-9398-1

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Cited by: 5 works

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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

An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty
journal, June 2018

Kolvenbach, Philip; Lass, Oliver; Ulbrich, Stefan
Optimization and Engineering, Vol. 19, Issue 3
DOI: 10.1007/s11081-018-9388-3

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

Adam, L.; Hintermüller, M.; Surowiec, T. M.
Optimization and Engineering, Vol. 19, Issue 3
DOI: 10.1007/s11081-018-9394-5

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

An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty
journal, June 2018

Kolvenbach, Philip; Lass, Oliver; Ulbrich, Stefan
Optimization and Engineering, Vol. 19, Issue 3
DOI: 10.1007/s11081-018-9388-3

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

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Title: An introduction to partial differential equations constrained optimization

Abstract

Citation Formats

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