Multigrid Methods for Elliptic Optimal Control Problems with Neumann Boundary Control

Stefan Takacs () and Walter Zulehner ()
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Stefan Takacs: Johannes Kepler University Linz, Doctoral Program Computational Mathematics
Walter Zulehner: Johannes Kepler University Linz, Institute of Computational Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 855-863 from Springer

Abstract: Abstract In this article we discuss multigrid methods for solving discretized optimality systems for elliptic optimal control problems. We concentrate on a model problem of tracking type with Neumann boundary control, whose optimality system is a linear system for the state y, the control u and the adjoined state p. An Uzawa-type smoother is used for the multigrid method. Moreover, we will compare this approach with standard smoothers, like damped Jacobi iteration applied to the normal equation of the Karush–Kuhn–Tucker system. A rigorous multigrid convergence analysis is presented for both smoothers.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_92

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DOI: 10.1007/978-3-642-11795-4_92

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