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A Brief Introduction to PDE-Constrained Optimization

  • Harbir Antil
  • Dmitriy Leykekhman
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 163)

Abstract

In this chapter we give a brief overview of optimization problems with partial differential equation (PDE) constraints, i.e., PDE-constrained optimization (PDECO). We start with three potentially different formulations of a general PDECO problem and focus on the so-called reduced form. We present a derivation of the optimality conditions. Later we discuss the linear and the semilinear quadratic PDECO problems. We conclude with the discretization and the convergence rates for these problems. For illustration, we make a MATLAB code available at

https://bitbucket.org/harbirantil/pde_constrained_opt that solves the semilinear PDECO problem with control constraints.

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Authors and Affiliations

  1. 1.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA

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