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MiS Preprint
68/2008
Quasiconvex relaxation of multidimensional control problems with integrands $f(t,\xi,v)$
Marcus Wagner
Abstract
We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands $f(t, \xi, v)$ 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 The relaxed problem, wherein the integrand $f$ has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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.
Quasiconvex functions with infinite values, lower semicontinuous quasiconvex envelope, multidimensional control problem, relaxation, existence of global minimizers, image registration, polyconvex regularization
Related publications
inJournal
2011
Repository Open Access
Marcus Wagner
Quasiconvex relaxation of multidimensional control problems with integrands f(t, e, v)
In: Control, optimisation and calculus of variations (ESAIM-COCV), 17 (2011) 1, pp. 190-221