Smoothing and interpolation in a convex subset of a Hilbert space : II. The semi-norm case
نویسندگان
چکیده
We improve upon results of our previous paper on interpolation subject to convex constramts In this paper we focus on the case of comtrained best interpolation when the object function is chosen to be \\ Tx || where T is a bounded hnear operator defined on a Hubert space X onto another Hilbert space Y with aftmte dimemional kernel ( We simpfy say T is correct from X to Y) We prove that under rather genet al circumstances this problem can be separated intofirst finding an orthogonal projection onto some constraint set and then solvmg a fimte dimensional min-max problem whose saddle point détermines the solution of our problem Resumé — On presente des résultats permettant d améliorer des théorèmes obtenus dans un article precedent Dans cet article on étudie le problème d'interpolation optimale sous contraintes obtenue quand on minimise une semi-norme || Tx || Ici T est un operateur lineaire borne et surjectif défini dans un espace de Hubert X dans un autre espace de Hubert Y ayant un noyau de dimension finie On démontre que, sous des hypotheses assez génerales, ce problème peut être décompose en une projection orthogonale sur un certain ensemble convexe suivie de la resolution d'un problème de mm-max en dimension finie le point de selle determinant la solution de notre problème
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