Solving Elliptic Control Problems with Interior Point and SQP Methods:
Control and State Constraints

by

Hans D. Mittelmann

Arizona State University

Department of Mathematics

Tempe, AZ 85287-1804, USA

E-mail: mittelmann@asu.edu

and

Helmut Maurer

Westfälische Wilhelms-Universität Münster

Institut für Numerische und instrumentelle Mathematik

Einsteinstrasse 62, 48149 Münster, Germany

E-mail: maurer@math.uni-muenster.de

Hans D. Mittelmann

Arizona State University

Department of Mathematics

Tempe, AZ 85287-1804, USA

E-mail: mittelmann@asu.edu

and

Helmut Maurer

Westfälische Wilhelms-Universität Münster

Institut für Numerische und instrumentelle Mathematik

Einsteinstrasse 62, 48149 Münster, Germany

E-mail: maurer@math.uni-muenster.de

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.

Keywords

Elliptic control problems, boundary and distributed control,
control and state constraints, discretization techniques,
interior point optimization methods

- Introduction
- Necessary conditions for elliptic control problems with control and state constraints
- Discretization and optimization techniques
- Numerical examples
- Bibliography
- About this document ...

2000-12-09