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Numerical PDE-Constrained Optimization

  • Book
  • © 2015

Overview

Authors:
  1. Juan Carlos De los Reyes

    1. Escuela Politécnica Nacional Quito, Quito, Ecuador

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  • Clear exposition of first and second order optimality conditions for PDE-constrained optimization problems
  • Careful and accessible presentation of optimization methods for solving PDE-constrained optimization problems, including MATLAB codes
  • Analytical and numerical treatment of representative nonsmooth PDE-constrained optimization problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Juan Carlos De los Reyes
    Pages 1-8

  3. Basic Theory of Partial Differential Equations and Their Discretization

    • Juan Carlos De los Reyes
    Pages 9-23

  4. Theory of PDE-Constrained Optimization

    • Juan Carlos De los Reyes
    Pages 25-41

  5. Numerical Optimization Methods

    • Juan Carlos De los Reyes
    Pages 43-68

  6. Box-Constrained Problems

    • Juan Carlos De los Reyes
    Pages 69-90

  7. Nonsmooth PDE-Constrained Optimization

    • Juan Carlos De los Reyes
    Pages 91-118

  8. Back Matter

    Pages 119-123
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Keywords

About this book

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

Authors and Affiliations

  • Escuela Politécnica Nacional Quito, Quito, Ecuador

    Juan Carlos De los Reyes

About the author

Juan Carlos De los Reyes is a Director of the Research Center on Mathematical Modelling (MODEMAT), and Professor of Optimization and Control at Escuela Politecnica Nacional.

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