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Mesh-independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems
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posted on 2023-06-08, 05:27 authored by M HintermuellerA class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual active-set method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-set method in function space is established, and its mesh independence is proved. The paper contains a report on numerical test runs including a comparison with a short-step path-following interior-point method and a coarse-to-fine mesh sweep, that is, a nested iteration technique, for accelerating the overall solution process. Finally, convergence and regularity properties of the regularized problems with respect to a vanishing Lavrentiev parameter are considered.
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Publication status
- Published
Journal
ANZIAM JournalISSN
1446-8735Publisher
Australian Mathematical SocietyIssue
1Volume
49Page range
1-38Department affiliated with
- Mathematics Publications
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Unable to access PDF due to server error.Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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