Solving elliptic control problems with interior point and SQP methods: Control and state constraints

Hans Mittelmann, Helmut Maurer

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We study optimal control problems for semilinear elliptic equations subject to control and state inequality constraints. Both boundary control and distributed control problems are considered with boundary conditions of Dirichlet or Neumann type. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. Necessary conditions of optimality are discussed both for the continuous and the discretized control problem. It is shown that the recently developed interior point method LOQO of [35] is capable of solving these problems even for high discretizations. Four numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for different types of controls including bang-bang controls. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish (US)
Pages (from-to)175-195
Number of pages21
JournalJournal of Computational and Applied Mathematics
Volume120
Issue number1-2
DOIs
StatePublished - Aug 1 2000

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Keywords

  • Boundary and distributed control
  • Control and state constraints
  • Discretization techniques
  • Elliptic control problems
  • Interior point optimization methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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