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 language | English (US) |
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Pages (from-to) | 175-195 |
Number of pages | 21 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 120 |
Issue number | 1-2 |
DOIs | |
State | Published - Aug 2000 |
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