| Issue |
ESAIM: COCV
Volume 17, Number 1, January-March 2011
|
|
|---|---|---|
| Page(s) | 190 - 221 | |
| DOI | https://doi.org/10.1051/cocv/2010008 | |
| Published online | 31 March 2010 | |
Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)
University of Graz, Institute for
Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria. www.thecitytocome.de; marcus.wagner@uni-graz.at
Received:
27
October
2008
We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration problem with convex and polyconvex regularization terms.
Mathematics Subject Classification: 26B05 / 26B25 / 49J20 / 49J45 / 68U10
Key words: Quasiconvex functions with infinite values / lower semicontinuous quasiconvex envelope / multidimensional control problem / relaxation / existence of global minimizers / image registration / polyconvex regularization
© 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.