| Issue |
ESAIM: M2AN
Volume 45, Number 3, May-June 2011
|
|
|---|---|---|
| Page(s) | 505 - 522 | |
| DOI | https://doi.org/10.1051/m2an/2010064 | |
| Published online | 11 October 2010 | |
Minimal invasion: An optimal L∞ state constraint problem
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, North Carolina, 27695-8205, USA.
kito@math.ncsu.edu
Received:
27
January
2010
Revised:
14
June
2010
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and well-posedness and superlinear convergence of the Newton method is shown. Numerical examples illustrate the features of this problem and the proposed approach.
Mathematics Subject Classification: 49J52 / 49J20 / 49K20
Key words: Optimal control / optimal L∞ state constraint / semi-smooth Newton method
© EDP Sciences, SMAI, 2010
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.