Titelaufnahme

Titel
Mesh independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems
Verfasser/ VerfasserinHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen
Erschienen in
The ANZIAM Journal, Cambridge, 2007, Jg. 49, H. 1, S. 1-38
ErschienenCambridge Univ. Press
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Active-set strategy / mesh-independence / mixed control-state constraints / PDE constraints / primal-dual methods / semi-smooth Newton methods
ISSN1446-8735
URNurn:nbn:at:at-ubg:3-1139 Persistent Identifier (URN)
DOIdoi:10.1017/S1446181100012657 
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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 [2.04 mb]
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Zusammenfassung (Englisch)

A 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 activeset 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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