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Weiser, Martin ; Gänzler, Tobias ; Schiela, Anton:
A control reduced primal interior point method for a class of control constrained optimal control problems.
In: Computational Optimization and Applications.
Bd. 41
(2008)
Heft 1
.
- S. 127-145.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-007-9088-y
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID DFG Research Center Matheon "Mathematics for key technologies" FZT 86 |
|---|---|
| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparatively coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.