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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

Published online by Cambridge University Press:  17 February 2009

M. Hintermüller
M. Hintermüller
Affiliation:
Department of Mathematics and Scientific Computing University of GrazHeinrichstr 36 A-8010 Graz [email protected].
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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. 2000 Mathematics subject classification: primary 65K05; secondary 90C33.

Keywords

Active-set strategymesh-independencemixed control-state constraintsPDE constraintsprimal-dual methodssemi-smooth Newton methods
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 1 - 38
Copyright
Copyright © Australian Mathematical Society 2007

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