Volume 46, Number 4, July-August 2012
|Page(s)||911 - 927|
|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
2 Department of Mathematics, North Carolina State University, Raleigh, 27695-8205, North Carolina, USA
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.