Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints: Part 1. Boundary Control

Authors:
Helmut Maurer;Hans D. Mittelmann
Affiliations:
Westfälische Wilhelms-Universität Münster, Institut für Numerische und instrumentelle Mathematik, Einsteinstrasse 62, 48149 Münster, Germany;Arizona State University, Department of Mathematics, Tempe, AZ 85287-1804, USA
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

We study optimal control problems for semilinear elliptic equations subject to control and state inequality constraints. In a first part we consider boundary control problems with either Dirichlet or Neumann conditions. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. It is shown that a recently developed interior point method is able to solve these 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 and singular controls. The necessary conditions of optimality are checked numerically in the presence of active control and state constraints.