ANZIAM J. 49 (2007), no. 1, pp. 1–38.

Mesh independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems

M. Hintermüller
Department of Mathematics and Scientific Computing
University of Graz
Heinrichstr. 36
A-8010 Graz
Austria
michael.hintermueller@uni-graz.at.
Received 28 April, 2007

Abstract

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 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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2000 Mathematics Subject Classification: primary 65K05; secondary 90C33
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2378147 Z'blatt-MATH: pre05243889

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