Frontiers in PDE-Constrained Optimization

  • Harbir Antil
  • Drew P. Kouri
  • Martin-D. Lacasse
  • Denis Ridzal

Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 163)

Table of contents

  1. Front Matter
    Pages i-x
  2. PDE-Constrained Optimization: Tutorials

    1. Front Matter
      Pages 1-1
    2. Harbir Antil, Dmitriy Leykekhman
      Pages 3-40
    3. Drew P. Kouri, Alexander Shapiro
      Pages 41-81
    4. Drew P. Kouri, Denis Ridzal
      Pages 83-121
    5. Jeremy Brandman, Huseyin Denli, Dimitar Trenev
      Pages 171-203
    6. Martin-D. Lacasse, Laurent White, Huseyin Denli, Lingyun Qiu
      Pages 205-255
  3. PDE-Constrained Optimization: Applications

About this book


This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics.  

This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. We place special emphasis on algorithm development and numerical computation.

The second part of this volume focuses on the application of PDE-constrained optimization including problems in optimal control, optimal design and inverse problems, which includes a comprehensive treatment of inverse problems arising in the oil and gas industry, among other topics.


PDE Constrained Optimization Optimal Control of PDEs Trust Region Methods Shape Optimization Sparsity in Inverse Problems Sequential Quadratic Programming PDE Constrained Optimization in Oil Industry Optimal Transport and Seismic Imaging

Editors and affiliations

  • Harbir Antil
    • 1
  • Drew P. Kouri
    • 2
  • Martin-D. Lacasse
    • 3
  • Denis Ridzal
    • 4
  1. 1.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA
  2. 2.Center for Computing Research, Sandia National LaboratoriesAlbuquerqueUSA
  3. 3.Corporate Strategic ResearchExxonMobil Research and Engineering CompanyAnnandaleUSA
  4. 4.Center for Computing Research, Sandia National LaboratoriesAlbuquerqueUSA

Bibliographic information

  • DOI
  • 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
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Print ISBN 978-1-4939-8635-4
  • Online ISBN 978-1-4939-8636-1
  • Series Print ISSN 0940-6573
  • Series Online ISSN 2198-3224
  • Buy this book on publisher's site
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