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An introduction to partial differential equations constrained optimization

Journal Article · · Optimization and Engineering
 [1];  [2]
  1. Technische Univ. of Munich (Germany)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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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.
Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1478062
Report Number(s):
SAND--2018-8151J; 666187
Journal Information:
Optimization and Engineering, Journal Name: Optimization and Engineering Journal Issue: 3 Vol. 19; ISSN 1389-4420
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

References (8)

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
Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting journal June 2018
Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation journal June 2018
PDE-constrained optimization in medical image analysis journal June 2018
Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics journal June 2018
A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn–Hilliard–Navier–Stokes system journal June 2018
A PDE-constrained optimization approach for topology optimization of strained photonic devices journal July 2018
Designing polymer spin packs by tailored shape optimization techniques journal June 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING