Preprint series: 05-04, Reports on Optimization and Stochastics

MSC:

52A20 Convex sets in $n$ dimensions (including convex hypersurfaces), See also {53A07, 53C45}

40A05 Convergence and divergence of series and sequences

49J45 Problems involving semicontinuity and convergence

Abstract: We investigate two types of semicontinuity for set-valued maps, Painlevé-Kuratowski
semicontinuity and Cesari's property (Q). It is shown that, in the context of
convex-valued maps, the concepts related to Cesari's property (Q) have better
properties than the concepts in the sense of Painlevé-Kuratowski.
In particular, we give a characterization of Cesari's property (Q) by
means of upper semicontinuity of the scalarizations by the support
function. We compare both types of semicontinuity and show their coincidence in special cases.

Keywords: set convergence, set-valued maps, continuity, Q-convergence, property Q

Notes: Old title: Semicontinuity of Convex-valued Multifunctions

Upload: 2005-05-02

Update: 2005 -11 -22