| Issue |
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
|
|
|---|---|---|
| Page(s) | 911 - 927 | |
| DOI | https://doi.org/10.1051/m2an/2011074 | |
| Published online | 03 February 2012 | |
A minimum effort optimal control problem for elliptic PDEs
1 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
christian.clason@uni-graz.at; karl.kunisch@uni-graz.at
2 Department of Mathematics, North Carolina State University, Raleigh, 27695-8205, North Carolina, USA
kito@math.ncsu.edu
Received: 2 February 2011
Revised: 22 September 2011
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.
Mathematics Subject Classification: 49J52 / 49J20 / 49K20
Key words: Optimal control / minimum effort / L∞control cost / semi-smooth Newton method
© EDP Sciences, SMAI, 2012
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