Multigrid Methods for Control-Constrained Elliptic Optimal Control Problems

Michelle Vallejos () and Alfio Borzì ()
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Michelle Vallejos: University of the Philippines, Institute of Mathematics
Alfio Borzì: Università degli Studi del Sannio, Dipartimento e Facoltà di Ingegneria

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 883-891 from Springer

Abstract: Abstract Multigrid schemes that solve control-constrained elliptic optimal control problems discretized by finite differences are presented. A gradient projection method is used to treat the constraints on the control variable. A comparison is made between two multigrid methods, the multigrid for optimization (MGOPT) method and the collective smoothing multigrid (CSMG) method. To illustrate both techniques, we focus on minimization problems governed by elliptic differential equations with constraints on the control variable.

Keywords: Optimal Control Problem; Optimality System; Multigrid Method; Gradient Projection Method; Smoothing Algorithm (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_95

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DOI: 10.1007/978-3-642-11795-4_95

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