**Optimization Techniques for Solving Elliptic Control
Problems with Control and State Constraints.
Part 2: Distributed Control
**

HELMUT MAURER

*Westfälische Wilhelms-Universität Münster,
Institut für Numerische und
instrumentelle Mathematik,
Einsteinstrasse 62, 48149 Münster, Germany
*

HANS D. MITTELMANN

*Arizona State University, Department of Mathematics, Tempe, AZ 85287-1804, USA
*

**Abstract:**
Part 2 continues the study of optimization techniques for elliptic control
problems subject to control and state constraints and is devoted
to *distributed* control.
Boundary conditions are of mixed Dirichlet and Neumann type.
Necessary conditions of optimality are formally stated in form of a
local Pontryagin minimum principle.
By introducing suitable discretization schemes, the control problem
is transcribed into a
nonlinear programming problem.
The problems are formulated as AMPL [13] scripts and several
optimization codes are applied.
In particular, it is shown that a recently developed interior point method
is able to solve theses problems even for high discretizations.
Several 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.
The necessary conditions of optimality are checked numerically in the
presence of active control and state constraints.

**Key words:** Elliptic control problems, distributed control,
control and state constraints, discretization techniques,
NLP-methods

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

2000-10-06