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

Hintermueller, M (2007) Mesh-independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems. ANZIAM Journal, 49 (1). pp. 1-38. ISSN 1446-8735

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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.

Item Type: Article
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Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: EPrints Services
Date Deposited: 06 Feb 2012 20:13
Last Modified: 10 Jul 2012 09:00
URI: http://sro.sussex.ac.uk/id/eprint/24729
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