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A minimum effort optimal control problem for elliptic PDEs

Published online by Cambridge University Press:  03 February 2012

Christian Clason ,
Kazufumi Ito  and
Karl Kunisch
Christian Clason
Affiliation:
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. christian.clason@uni-graz.at; karl.kunisch@uni-graz.at
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, 27695-8205, North Carolina, USA; kito@math.ncsu.edu
Karl Kunisch
Affiliation:
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. christian.clason@uni-graz.at; karl.kunisch@uni-graz.at

Abstract

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This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation illustrate the behavior of minimum effort controls.

Keywords

Optimal controlminimum effortL∞control costsemi-smooth Newton method

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 911 - 927
Copyright
© EDP Sciences, SMAI, 2012

References

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